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\PR$NaRA G F 0AA@3ʚ;ʚ;g4BdBd$v}0(ppp@ <4ddddPa0֞ 80___PPT10 ppHModern akola CZ.1.07/1.5.00/34.0827$%HMatematika 5.4  Posloupnosti a Yady%%Autor:PaedDr. JiY Kocman Nzev: 5.4.7 Aritmetick posloupnost  zkladn pojmy(P6Datum vytvoYen: 8.3. 2013 Clov skupina: }k gymnzia Vzdlvac oblast, vzdlvac obor: Matematika Anotace: Materil je ur en pro frontln prci se ~ky. Vklad novho u iva je prokldn vzorovmi pYklady, kter u itel Yea se ~ky nebo pYklady, kter Yea ~ci sami (v etn vsledko). Clem hodiny je zskn zkladnch dovednost pro prci se zkladnmi vztahy pro aritmetickou posloupnost. Sou st materilu je pracovn list slou~c pro procvi en a samostatnou prci ~ko.hpPwPg  /8  H @  (     <-_  > vodn loha   <L"`e j4 Rychlost aYen zvuku je pYi 0C 331 m/s S rostouc teplotou rovnomrn spojit roste PYi zvaen o 1C vzroste o 0,6 m/s Jak bude teplota pYi 5C ?-H  <G "`"%B `Ozna me vn rychlost v m/s pYi teplot (n  1)C01  & &  <"`R 8PYi 0C v1 = 331 PYi 1C v2 = v1 + 0,6 = 331 + 1 . 0,6 PYi 2C v3 = v2 + 0,6 = v1 + 2 . 0,6 = 331 + 2 . 0,6 PYi 3C v4 = v3 + 0,6 = v1 + 3 . 0,6 = 331 + 3 . 0,6 PYi 4C v5 = v4 + 0,6 = v1 + 4 . 0,6 = 331 + 4 . 0,6 PYi 5C v6 = v5 + 0,6 = v1 + 5 . 0,6 = 331 + 5 . 0,6 Rychlost pYi teplot 5C je 331 + 3 = 334 m/s.A    %    $    #    %    KH  0޽h ? 3380___PPT10.w%`!0 $0(  $H $ 0޽h ? 3380___PPT10.y%þr-> IS >8T   (    Rovnice Equation.30"Editor rovnic 3.0/ 0LDArial֞ Z 0 v}0"@ . @;!2BlJߔɀķf Оbr<"o4l!$~SM`AݯTCiG=?\Na`v0o(McdbR ,.Ieԡ[> 1,IS`!CsO k2@ 0xڥSKA~v.(v(:DFFiRPc P9/)kK0$y,J 7{߼y " [Șc14MӲVؤ/B0`3n 뙐 QGbT0.4#+7zoVM rWR'zQLN[pL X+]4~kƔ| hxy(o^oLת|_^,eomGb0ᴋdb8)Dk|>7?7En?" dd@  @@`` phX $ ) Ob$i,0t&(PR$V;,0V \PR$NaRA G F2$ s8/v 0AA@3ʚ;ʚ;g4BdBd$v}0(ppp@ <4ddddPa0֞ 80___PPT10 ppHModern akola CZ.1.07/1.5.00/34.0827$%HMatematika 5.4  Posloupnosti a Yady%%Autor:PaedDr. JiY Kocman Nzev: 5.4.7 Aritmetick posloupnost  zkladn pojmy(P6Datum vytvoYen: 8.3. 2013 Clov skupina: }k gymnzia Vzdlvac oblast, vzdlvac obor: Matematika Anotace: Materil je ur en pro frontln prci se ~ky. Vklad novho u iva je prokldn vzorovmi pYklady, kter u itel Yea se ~ky nebo pYklady, kter Yea ~ci sami (v etn vsledko). Clem hodiny je zskn z  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntrydO)T:pPicturesCCurrent User ASummaryInformation(!T    W c"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKMNOPQRSTUVXYZ[rbdefghijklmnLzstuvwxy{|}~PowerPoint Document( DocumentSummaryInformation8d@  @@`` <4P "?b$i,0t&(PR$V;,0V \PR$NaRA G F 0AA@3ʚ;ʚ;g4BdBd$v}0(ppp@ <4ddddPa0֞ 80___PPT10 ppHModern akola CZ.1.07/1.5.00/34.0827$%HMatematika 5.4  Posloupnosti a Yady%%Autor:PaedDr. JiY Kocman Nzev: 5.4.7 Aritmetick posloupnost  zkladn pojmy(P6Datum vytvoYen: 8.3. 2013 Clov skupina: }k gymnzia Vzdlvac oblast, vzdlvac obor: Matematika Anotace: Materil je ur en pro frontln prci se ~ky. Vklad novho u iva je prokldn vzorovmi pYklady, kter u itel Yea se ~ky nebo pYklady, kter Yea ~ci sami (v etn vsledko). Clem hodiny je zskn zkladnch dovednost pro prci se zkladnmi vztahy pro aritmetickou posloupnost. Sou st materilu je pracovn list slou~c pro procvi en a samostatnou prci ~ko.hpPwPg /8 `(  x  c $GU  x  c $PTG   T  C ,Adownload  C \ADOPVK_hor_zakladni_logolink_RGB_czf gt  \A޽h ?Balic papr"` 33___PPT10i.+D=' = @B +R  R(     <-_  > vodn loha   <L"`e j4 Rychlost aYen zvuku je pYi 0C 331 m/s S rostouc teplotou rovnomrn spojit roste PYi zvaen o 1C vzroste o 0,6 m/s Jak bude teplota pYi 5C ?-H  <G "`"%B `Ozna me vn rychlost v m/s pYi teplot (n  1)C01  & &,  <"`R PYi 0C v1 = 331 PYi 1C v2 = v1 + 0,6 = 331 + 1 . 0,6 PYi 2C v3 = v2 + 0,6 = v1 + 2 . 0,6 = 331 + 2 . 0,6 PYi 3C v4 = v3 + 0,6 = v1 + 3 . 0,6 = 331 + 3 . 0,6 PYi 4C v5 = v4 + 0,6 = v1 + 4 . 0,6 = 331 + 4 . 0,6 PYi 5C v6 = v5 + 0,6 = v1 + 5 . 0,6 = 331 + 5 . 0,6 Rychlost pYi teplot 5C je 331 + 3 = 334 m/s.AAH  0޽h ? 3380___PPT10.w%`!r '15&=  ( / 0LDArial֞ Z 0 v}0"@ . @n?" dd@  @@`` D<X$ # ?b$      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ՜.+,0    *Pedvdn na obrazovceDoma<   ArialVchoz nvrhEditor rovnic 3.0%Modern kola CZ.1.07/1.5.00/34.0827PAutor:PaedDr. Ji Kocman Nzev: 5.4.7 Aritmetick posloupnost zkladn pojmy  kladnch dovednost pro prci se zkladnmi vztahy pro aritmetickou posloupnost. Sou st materilu je pracovn list slou~c pro procvi en a samostatnou prci ~ko.hpPwPg  /8r   $r(  $l $ 0WY  rPosloupnost se nazv aritmetick prv tehdy, kdy~ existuje takov slo d, ~e pro ka~d len tto posloupnosti plat : an+1 = an + d. slo d se nazv: DIFERENCE posloupnostiJ  2,2 $ <r"`V * $ <^"`4 0Hodnoty v1, & , v5 tvoY posloupnost. Ka~d len tto posloupnosti zskme tak, ~e k pYedchozmu lenu pYi tme slo 0,6. Rozdl po sob jdoucch leno je stejn ( konstantn) :0,6 Je to pYklad tzv. ARITMETICK posloupnosti.J   ^  $ 6d  $ C A ?"?o    $ <ț"`< vDosledek: Pro vaechna pYirozen sla plat: an+1  an = d.V<&  ,-H $ 0޽h ? 3380___PPT10.y%þ xVMKQ=M,?Rj ՁqbX2b\0~DSb>L,+A7ݺJB K'[37yAD܈9M޻Μ{{}@3Mz]w3;m<*\sD;FOi!$1t4{^遼]ypR OSPvK~D!? g{(3 |h*SX~sC}o~u޼6X3PS18ɾ0 H`Žy` k kWZh?b~sT-jd [˗q3 =ܲ \{?*n2oSTm#TR_] *z͕ɱ .CeiD _c>ˆF3Yݜ~*<<{I^dtŨzF2Jay{Xwg0=7g"|[p_gɕӋHP)(Z?43 lcrxT ?`iTTk   (    Rovnice Equation.30"Editor rovnic 3.0/ 0LDArial֞ Z 0 v}0"@ . @n?" dd@  @@`Snmek 3 Snmek 4 Snmek 5 Snmek 6 Snmek 7 Snmek 8 Snmek 9 Pouit psma#_ Ji KocmanJiY Kocmanablona nvrhuVloen servery OLENadpisy snmk ` xp`( +   Ob$i,0t&(PR$V;,0V \PR$NaRA G F2$ s8/v 0AA@3ʚ;ʚ;g4BdBd$v}0(ppp@ <4ddddPa0֞ 80___PPT10 ppHModern akola CZ.1.07/1.5.00/34.0827$%HMatematika 5.4  Posloupnosti a Yady%%Autor:PaedDr. JiY Kocman Nzev: 5.4.7 Aritmetick posloupnost  zkladn pojmy(P6Datum vytvoYen: 8.3. 2013 Clov skupina: }k gymnzia Vzdlvac oblast, vzdlvac obor: Matematika Anotace: Materil je ur en pro frontln prci se ~ky. Vklad novho u iva je prokldn vzorovmi pYklady, kter u itel Yea se ~ky nebo pYklady, kter Yea ~ci sami (v etn vsledko). Clem hodiny je zskn zkladnch dovednost pro prci se zkladnmi vztahy pro aritmetickou posloupnost. Sou st materilu je pracovn list slou~c pro procvi en a samostatnou prci ~ko.hpPwPg   /8  H @  $(  $l $ 0WY  rPosloupnost se nazv aritmetick prv tehdy, kdy~ existuje takov slo d, ~e pro ka~d len tto posloupnosti plat : an+1 = an + d. slo d se nazv: DIFERENCE posloupnostiJ  2,2 $ <r"`V * $ <^"`4 0Hodnoty v1, & , v5 tvoY posloupnost. Ka~d len tto posloupnosti zskme tak, ~e k pYedchozmu lenu pYi tme slo 0,6. Rozdl po sob jdoucch leno je stejn ( konstantn) :0,6 Je to pYklad tzv. ARITMETICK posloupnosti.J   ^  $ 6d  $ C A ?"?o    $ <ț"`< vDosledek: Pro vaechna pYirozen sla plat: an+1  an = d.V<&  ,-^  $ 6H $ 0޽h ? 3380___PPT10.y%þ0 (0(  (H ( 0޽h ? 3380___PPT10.{%@? xVMKQ=M,?Rj ՁqbX2b\0~DSb>L,+A7ݺJB K'[37yAD܈9M޻Μ{{}@3Mz]w3;m<*\sD;FOi!$1t4{^遼]ypR OSPvK~D!? g{(3 |h*SX~sC}o~u޼6X3PS18ɾ0 H`Žy` k kWZh?b~sT-jd [˗q3 =ܲ \{?*n2oSTm#TR_] *z͕ɱ .CeiD _c>ˆF3Yݜ~*<<{I^dtŨzF2Jay{Xwg0=7g"|[p_gɕӋHP)(Z?43 lcrl 0xk6  (     "DxgXh>wgUac+!g#@{_>Ao,>sd6VR[qY;C՚C811 @v~2`!EWρHE<t^ 9xڥS=KAK4D B g Vb9p`-bN+ATRXX JDlJ"=905/ z-hɷb: yh50 g-f>5'j}^);0b+IV6jo  B~KNrvh@Ah NS.ı8"x;p*'C:{<18ňlPKYV'[grsP{y&zzzĿk!`29_T0R{X++\lh۪qhUԳ@왳0/PD7v(&Ccz`!{R.zO-@81xcdd``$d@9`,&FF(`T A?d@=P5< %!@5 @_L ĺEDA,a ˀ &&L ' gMa`XϕP!bD VpZ'm5FF\ Lj ~ _&m8P寱"O`Qq\%}LwNFX47$37X/\!(?71!2Aa )xA|J+|'o$3#Ec< 2!~=vd~/f?ηbHN {.p#nv0o(ϽcdbR ,.IeX C D,x,Ā`"V`!0jX޻P` lVv`w!9xcdd``$d@9`,&FF(`Ts A?dbA3zjx|K2B* Rj8 :@u!f0109Y@#ȝATN`gbM-VK-WMc<O{1lWHi% VrA]x `121)W20gPdkY&0h73X?!@`!a@YR] R pcxcdd``e 2 ĜL0##0KQ* W􀙁KRcgbR vE3zjx|K2B* Rj8 :@u!f0109Y@V;LL'AtO` ZZsy"+8|-ϗ& lWVJ?+oX aFeL I% \+0 #ltp~3*?o`$1\ `b2!nOU.p̃b;V121)W2ȂaPdk)y.Ā`t\`!1MgyGC:YͧÏ; pcxcdd``e 2 ĜL0##0KQ* W􀙁KRcgbR vE3zjx|K2B* Rj8 :@u!f0109Y@V;LL'AtO` ZZRovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0/ 0LDArial֞ Z 0 v}0"@ . @n?" dd@  @@`` TL`( <   b$i,0t&(PR$V;,0V \PR$NaRA G F2$ s8/v2$CsO k2$EWρHE<tu2${R.zO-t2$jX޻P` lV8U 2$a@YR] R! 0AA@3ʚ;ʚ;g4BdBd$v}0(ppp@ <4ddddPa0֞ 80___PPT10 ppHModern akola CZ.1.07/1.5.00/34.0827$%HMatematika 5.4  Posloupnosti a Yady%%Autor:PaedDr. JiY Kocman Nzev: 5.4.7 Aritmetick posloupnost  zkladn pojmy(P6Datum vytvoYen: 8.3. 2013 Clov skupina: }k gymnzia Vzdlvac oblast, vzdlvac obor: Matematika Anotace: Materil je ur en pro frontln prci se ~ky. Vklad novho u iva je prokldn vzorovmi pYklady, kter u itel Yea se ~ky nebo pYklady, kter Yea ~ci sami (v etn vsledko). Clem hodiny je zskn zkladnch dovednost pro prci se zkladnmi vztahy pro aritmetickou posloupnost. Sou st materilu je pracovn list slou~c pro procvi en a samostatnou prci ~ko.hpPwPg   /8  F > ( (  ( ( < j  9loha 1 ( <`"` T + b0Doka~te, ~e posloupnost ^ ( 6d ( C A ?"? R  ( <$"`<9 &je aritmetick. Ur ete jej diferenci. an+1  an = 2( n + 1)  4  ( 2n  4) = 2n + 2  4  2n + 4 = 2 Rozdl dvou po sob jdoucch leno je 2 (konstantn). Tedy se jedn o aritmetickou posloupnost s diferenc 2. ,'  ( <D`j  @Cvi en^  ( 6d  ( C A ?"? Z    ( <@"`  bRozhodnte, zda je dan posloupnost aritmetick?22  ( <P4 s =g  @Xeaen:^ ( 6d ( C A ?"? *  ^ ( 6j ( S A  ??"? p  ( 0,8"` Y'Posloupnost je aritmetick s diferenc ((^ ( 6d ( C A  ?"?i  H ( 0޽h ? 3380___PPT10.{%@? xVMKQ=M,?Rj ՁqbX2b\0~DSb>L,+A7ݺJB K'[37yAD܈9M޻Μ{{}@3Mz]w3;m<*\sD;FOi!$1t4{^遼]ypR OSPvK~D!? g{(3 |h*SX~sC}o~u޼6X3PS18ɾ0 H`Žy` k kWZh?b~sT-jd [˗q3 =ܲ \{?*n2oSTm#TR_] *z͕ɱ .CeiD _c>ˆF3Yݜ~*<<{I^dtŨzF2Jay{Xwg0=7g"|[p_gɕӋHP)(Z?43 lc xVOKA}3nP"H z 5)R[I`K, hbLlzi ]ȩ ~zړg^fw.)1/f~fff_l%:x|B7eYN-m=,OqdQvWz Oo;q0T_uqzaB o=~=˟f:!0U_~_}Ce_o(Z}nߧc=]o/t^?|VQ+7vYUDn}vD W3Gu+0xPc"'*1gf! HDa ٫CTٚlM2oPjܝܛbS9__@~)L'= ghtL=UY,U $iؖRdO㹝c4C=YG *zYi:jgɢmWa߁>RehyIwkW xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!xc[z$+SrRIp101"X}" 0e(#!dԧAP{=t 9e!~[a?h>+Tn8 b#00sAzEi% %y z <@)`73|TH Xv-&acx5@b sALfddbdPs"3?#7 ,yi00Mg320u3)4Y305*1\ |`AzzAz;L)i!XgK<`=U*#NP|͡(T : xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH! 9Ff<#LgaH%NdĈb0w?$, ORe3C~%AnPr`d`Zd@KJD?F`Ja悤=/$|3J\ KK2 xR.p1n 3fbX03ZL j* (Ԝ d10i30u202p1 )BDmAPn1ujA4F+dWBRD`ɟ ,}WFT =DLQS e` ;xXkA36#ZJ 1Қ Rh Ӓ`$mdA(Aov\9H^iVh b/j{Fvo:juaST,VT4]#fA? m)w r ow<3Gyp2RC~Hᮘ@fh549?twc5[d3\ %2@@HdMS!|B-LZ 2n{ZЍQ >$5Foݢ2;.Q渄N2Ƿ5 w h=h_>XR@k2Gs71W.gq}L֎XhTm=Gox.|O⡩~ {0u7١{yٸd@2ݑĐEB@A^XAӠlfOA`?ȭr4Fā>8 NI{y_Hf&秕(&d)0\b @>grS!.`f`!ڵ@Ԏ9$w3&S!4˘00 ) 5icS- HBJ`yfmtt ?X?(RYz;AeFQS eE?wr(z p% % V (     Rovnice Equation.30"Editor rovnic 3.0sy"+8|-7O{ lWVJ?+oX aFeL I% \ ~7p pw%0`a ׅQ1xp#q6 yp{ |.hrc =򎑉I)$5%E./B a 4uy`!Ĕ WSZ^ɳu @ac)|xcdd`` @c112BYL%bpu 1Dl\ _x^Usi#:Ff6VJB sm#d.'M DYd++&t'\F \ R*aj|?f?ηb!PO; Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0/ 0LDArial֞ Z 0 v}0"@ . @n?" dd@  @@`` h, =   b$i,0t&(PR$V;,0V \PR$NaRA G F2$ s8/v2$CsO k2$EWρHE<tu2${R.zO-t2$jX޻P` lV8U $2$1MgyGC:YͧÏ;*# 0AA@3ʚ;ʚ;g4BdBd$v}0(ppp@ <4ddddPa0֞ 80___PPT10 ppHModern akola CZ.1.07/1.5.00/34.0827$%HMatematika 5.4  Posloupnosti a Yady%%Autor:PaedDr. JiY Kocman Nzev: 5.4.7 Aritmetick posloupnost  zkladn pojmy(P6Datum vytvoYen: 8.3. 2013 Clov skupina: }k gymnzia Vzdlvac oblast, vzdlvac obor: Matematika Anotace: Materil je ur en pro frontln prci se ~ky. Vklad novho u iva je prokldn vzorovmi pYklady, kter u itel Yea se ~ky nebo pYklady, kter Yea ~ci sami (v etn vsledko). Clem hodiny je zskn zkladnch dovednost pro prci se zkladnmi vztahy pro aritmetickou posloupnost. Sou st materilu je pracovn list slou~c pro procvi en a samostatnou prci ~ko.hpPwPg   /8  F > ( (  ( ( < j  9loha 1 ( <`"` T + b0Doka~te, ~e posloupnost ^ ( 6d ( C A ?"? R  ( <$"`<9 &je aritmetick. Ur ete jej diferenci. an+1  an = 2( n + 1)  4  ( 2n  4) = 2n + 2  4  2n + 4 = 2 Rozdl dvou po sob jdoucch leno je 2 (konstantn). Tedy se jedn o aritmetickou posloupnost s diferenc 2. ,'  ( <D`j  @Cvi en^  ( 6d  ( C A ?"? Z    ( <@"`  bRozhodnte, zda je dan posloupnost aritmetick?22  ( <P4 s =g  @Xeaen:^ ( 6d ( C A ?"? *  ^ ( 6j ( S A  ??"? p  ( 0,8"` Y'Posloupnost je aritmetick s diferenc ((^ ( 6d ( C A  ?"?i  H ( 0޽h ? 3380___PPT10.{%@?0 ,0(  ,H , 0޽h ? 3380___PPT10.% xVMKQ=M,?Rj ՁqbX2b\0~DSb>L,+A7ݺJB K'[37yAD܈9M޻Μ{{}@3Mz]w3;m<*\sD;FOi!$1t4{^遼]ypR OSPvK~D!? g{(3 |h*SX~sC}o~u޼6X3PS18ɾ0 H`Žy` k kWZh?b~sT-jd [˗q3 =ܲ \{?*n2oSTm#TR_] *z͕ɱ .CeiD _c>ˆF3Yݜ~*<<{I^dtŨzF2Jay{Xwg0=7g"|[p_gɕӋHP)(Z?43 lc xVOKA}3nP"H z 5)R[I`K, hbLlzi ]ȩ ~zړg^fw.)1/f~fff_l%:x|B7eYN-m=,OqdQvWz Oo;q0T_uqzaB o=~=˟f:!0U_~_}Ce_o(Z}nߧc=]o/t^?|VQ+7vYUDn}vD W3Gu+0xPc"'*1gf! HDa ٫CTٚlM2oPjܝܛbS9__@~)L'= ghtL=UY,U $iؖRdO㹝c4C=YG *zYi:jgɢmWa߁>RehyIwkW xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!xc[z$+SrRIp101"X}" 0e(#!dԧAP{=t 9e!~[a?h>+Tn8 b#00sAzEi% %y z <@)`73|TH Xv-&acx5@b sALfddbdPs"3?#7 ,yi00Mg320u3)4Y305*1\ |`AzzAz;L)i!XgK<`=U*#NP|͡(T : xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH! 9Ff<#LgaH%NdĈb0w?$, ORe3C~%AnPr`d`Zd@KJD?F`Ja悤=/$|3J\ KK2 xR.p1n 3fbX03ZL j* (Ԝ d10i30u202p1 )BDmAPn1ujA4F+dWBRD`ɟ ,}WFT =DLQS e` ;xXKTQ?91$LBmDEa - E̐1*oP-\MD;[IItD! E3s}77* w:{V?YE΁t :ʘA@,Ki>Ɂ>/A'PTChU.WKUVpN>gKW 8(cp+gwӧ 5~#ً'xM;"%?dr|pH>OލѳO:x/wN)źx &`BQD_ @f\2raMCwœqӁp/\[ſӹ\//dsƟ\W)h?R#_n~.} Gg=}:FTx>'YΡր.xΩ]ct<.j i%8cRcZev;?_@vjv͌2>+f"|'9`VC ت8NE*Tl{AKǡb`4 g}h(חΆ vn;EL?L??жkclK-vYPHvmp`x0N71e`@F@2ݑĐEB@A^XAӠlfOA`?ȭr4Fā>8 NI{y_Hf&秕(&d)0\b @>grS!.`f`!ڵ@Ԏ9$w3&S!4˘00 ) 5icS- HBJ`yfmtt ?X?(RYz;AeFQS eE?wr,  <A" G(     Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0b/þ/BD88ܮOX@|m8_ ķ X2#(l,s BӴ;W121)W2ԡ"f|b@3X?y`!IӏÓ  @H7|qxcdd``ed``baV d,FYzP1n:&B@?b  ㆪaM,,He`Hc&,eBܤI\'>1Dl\ _˽ӸX u9W HF%!Np-m#dn0'M DYd++&t'\F \ R*a ~O1o 'V >] s0 ##O3> pO%; Cgam+ MJ+KRs@`Pdk[> 13X?ȣL`!^cYJ;-R @|sxcdd``^ @c112BYL%bpu Rvp۫ 0\N`AӞ;121)W2ĀePdh- i`!V"*Rf:T˹D  Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0 Rovnice Equation.30"Editor rovnic 3.0/ 0LDArial֞ Z 0 v}0"@ . @n?" dd@  @@`` h , D    b$i,0t&(PR$V;,0V \PR$NaRA G F2$ s8/v2$CsO k2$EWρHE<tu2${R.zO-t2$jX޻P` lV8U 2$Ĕ WSZ^ɳu$2$1MgyGC:YͧÏ;*#2$IӏÓ }& 0AA@3ʚ;ʚ;g4BdBd$v}0(ppp@ <4ddddPa0֞ 80___PPT10 ppHModern akola CZ.1.07/1.5.00/34.0827$%HMatematika 5.4  Posloupnosti a Yady%%Autor:PaedDr. JiY Kocman Nzev: 5.4.7 Aritmetick posloupnost  zkladn pojmy(P6Datum vytvoYen: 8.3. 2013 Clov skupina: }k gymnzia Vzdlvac oblast, vzdlvac obor: Matematika Anotace: Materil je ur en pro frontln prci se ~ky. Vklad novho u iva je prokldn vzorovmi pYklady, kter u itel Yea se ~ky nebo pYklady, kter Yea ~ci sami (v etn vsledko). Clem hodiny je zskn zkladnch dovednost pro prci se zkladnmi vztahy pro aritmetickou posloupnost. Sou st materilu je pracovn list slou~c pro procvi en a samostatnou prci ~ko.hpPwPg   /8 um ,(  , , </ vNeche jsou n, r, s pYirozen sla. Pak v ka~d A.P. plat:<<j , C A   ?#" `?P  ^ , 6j , C A   ?#" `?/P=  |  , < `  Pozn. Prvn ze vztaho bude dokzn matematickou indukc v pracovnm listu. Druh vztah vychz z prvnho."je  , <l  9loha 26  , <H% +  V A.P. je tYet len 5 a osm 15. Ur ete diferenci, prvn a sedmnct len.MMH , 0޽h ? 3380___PPT10.% xVMKQ=M,?Rj ՁqbX2b\0~DSb>L,+A7ݺJB K'[37yAD܈9M޻Μ{{}@3Mz]w3;m<*\sD;FOi!$1t4{^遼]ypR OSPvK~D!? g{(3 |h*SX~sC}o~u޼6X3PS18ɾ0 H`Žy` k kWZh?b~sT-jd [˗q3 =ܲ \{?*n2oSTm#TR_] *z͕ɱ .CeiD _c>ˆF3Yݜ~*<<{I^dtŨzF2Jay{Xwg0=7g"|[p_gɕӋHP)(Z?43 lc xVOKA}3nP"H z 5)R[I`K, hbLlzi ]ȩ ~zړg^fw.)1/f~fff_l%:x|B7eYN-m=,OqdQvWz Oo;q0T_uqzaB o=~=˟f:!0U_~_}Ce_o(Z}nߧc=]o/t^?|VQ+7vYUDn}vD W3Gu+0xPc"'*1gf! HDa ٫CTٚlM2oPjܝܛbS9__@~)L'= ghtL=UY,U $iؖRdO㹝c4C=YG *zYi:jgɢmWa߁>RehyIwkW xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!xc[z$+SrRIp101"X}" 0e(#!dԧAP{=t 9e!~[a?h>+Tn8 b#00sAzEi% %y z <@)`73|TH Xv-&acx5@b sALfddbdPs"3?#7 ,yi00Mg320u3)4Y305*1\ |`AzzAz;L)i!XgK<`=U*#NP|͡(T : xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH! 9Ff<#LgaH%NdĈb0w?$, ORe3C~%AnPr`d`Zd@KJD?F`Ja悤=/$|3J\ KK2 xR.p1n 3fbX03ZL j* (Ԝ d10i30u202p1 )BDmAPn1ujA4F+dWBRD`ɟ ,}WFT =DLQS e` ;xXKTQ?91$LBmDEa - E̐1*oP-\MD;[IItD! E3s}77* w:{V?YE΁t :ʘA@,Ki>Ɂ>/A'PTChU.WKUVpN>gKW 8(cp+gwӧ 5~#ً'xM;"%?dr|pH>OލѳO:x/wN)źx &`BQD_ @f\2raMCwœqӁp/\[ſӹ\//dsƟ\W)h?R#_n~.} Gg=}:FTx>'YΡր.xΩ]ct<.j i%8cRcZev;?_@vjv͌2>+f"|'9`VC ت8NE*Tl{AKǡb`4 g}h(חΆ vn;EL?L??жkclK-vYPHvmp`x0N71e`@F@2ݑĐEB@A^XAӠlfOA`?ȭr4Fā>8 NI{y_Hf&秕(&d)0\b @>grS!.`f`!ڵ@Ԏ9$w3&S!4˘00 ) 5icS- HBJ`yfmtt ?X?(RYz;AeFQS eE?w xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!}A#3+SrRIp101"X}" 0e(#!dԧAP{=t 9e!~[a?h>+= FE&EXL-\ŁofrQ~q~ZkaibIf~P%. 8z _,7f] d@CP~Üb<A.6[(S!TT$ eLmBJ` i@ dUjN ?X?(RYz;AUBQS e _;Y xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!m{A#3+SrRIp101"X}" 0e(#!dԧAP{=t 9e!~[a?h>+= FE&EXL-\ŁofrQ~q~ZkaibIf~P%. 8z _,7f] d@CP~8c1Ɍ\\B͉ @V1 S-hTT$ eLmBJ` i@ dPVZWBRD`ɟ ,}WFT =D*(T };r4z  e?V) (   H $xcdd``ed``baV d,FYzP1n: B@?b u 10 ㆪaM,,He`0 01d++&1Dl\ _w𥱰si#O )1d#d\J_/ CS,2@penR~C ?WB8n mS8dlMia(9#RpeqIj. 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Vklad novho u iva je prokldn vzorovmi pYklady, kter u itel Yea se ~ky nebo pYklady, kter Yea ~ci sami (v etn vsledko). Clem hodiny je zskn zkladnch dovednost pro prci se zkladnmi vztahy pro aritmetickou posloupnost. Sou st materilu je pracovn list slou~c pro procvi en a samostatnou prci ~ko.hpPwPg   /8  W O , (  , , </ vNeche jsou n, r, s pYirozen sla. Pak v ka~d A.P. plat:<<j , C A   ?#" `?P  ^ , 6j , C A   ?#" `?/P=  |  , < `  Pozn. Prvn ze vztaho bude dokzn matematickou indukc v pracovnm listu. Druh vztah vychz z prvnho."je  , <l  9loha 26  , <H% +  V A.P. je tYet len 5 a osm 15. Ur ete diferenci, prvn a sedmnct len.MM^  , 6((j  , C A   ?#" `?    ^ , 677j , C A   ?#" `?|    ^ , 677j , C A ?#" `? G ^ , 6((j , C A ?#" `? ~   ^ , 6((j , C A ?#" `? | r  ^ , 6++j , C A ?#" `? s ^ , 6((d , C A ?"? U H , 0޽h ? 3380___PPT10.% xVMKQ=M,?Rj ՁqbX2b\0~DSb>L,+A7ݺJB K'[37yAD܈9M޻Μ{{}@3Mz]w3;m<*\sD;FOi!$1t4{^遼]ypR OSPvK~D!? g{(3 |h*SX~sC}o~u޼6X3PS18ɾ0 H`Žy` k kWZh?b~sT-jd [˗q3 =ܲ \{?*n2oSTm#TR_] *z͕ɱ .CeiD _c>ˆF3Yݜ~*<<{I^dtŨzF2Jay{Xwg0=7g"|[p_gɕӋHP)(Z?43 lc xVOKA}3nP"H z 5)R[I`K, hbLlzi ]ȩ ~zړg^fw.)1/f~fff_l%:x|B7eYN-m=,OqdQvWz Oo;q0T_uqzaB o=~=˟f:!0U_~_}Ce_o(Z}nߧc=]o/t^?|VQ+7vYUDn}vD W3Gu+0xPc"'*1gf! HDa ٫CTٚlM2oPjܝܛbS9__@~)L'= ghtL=UY,U $iؖRdO㹝c4C=YG *zYi:jgɢmWa߁>RehyIwkW xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!xc[z$+SrRIp101"X}" 0e(#!dԧAP{=t 9e!~[a?h>+Tn8 b#00sAzEi% %y z <@)`73|TH Xv-&acx5@b sALfddbdPs"3?#7 ,yi00Mg320u3)4Y305*1\ |`AzzAz;L)i!XgK<`=U*#NP|͡(T : xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH! 9Ff<#LgaH%NdĈb0w?$, ORe3C~%AnPr`d`Zd@KJD?F`Ja悤=/$|3J\ KK2 xR.p1n 3fbX03ZL j* (Ԝ d10i30u202p1 )BDmAPn1ujA4F+dWBRD`ɟ ,}WFT =DLQS e` ;xXKTQ?91$LBmDEa - E̐1*oP-\MD;[IItD! E3s}77* w:{V?YE΁t :ʘA@,Ki>Ɂ>/A'PTChU.WKUVpN>gKW 8(cp+gwӧ 5~#ً'xM;"%?dr|pH>OލѳO:x/wN)źx &`BQD_ @f\2raMCwœqӁp/\[ſӹ\//dsƟ\W)h?R#_n~.} Gg=}:FTx>'YΡր.xΩ]ct<.j i%8cRcZev;?_@vjv͌2>+f"|'9`VC ت8NE*Tl{AKǡb`4 g}h(חΆ vn;EL?L??жkclK-vYPHvmp`x0N71e`@F@2ݑĐEB@A^XAӠlfOA`?ȭr4Fā>8 NI{y_Hf&秕(&d)0\b @>grS!.`f`!ڵ@Ԏ9$w3&S!4˘00 ) 5icS- HBJ`yfmtt ?X?(RYz;AeFQS eE?w xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!}A#3+SrRIp101"X}" 0e(#!dԧAP{=t 9e!~[a?h>+= FE&EXL-\ŁofrQ~q~ZkaibIf~P%. 8z _,7f] d@CP~Üb<A.6[(S!TT$ eLmBJ` i@ dUjN ?X?(RYz;AUBQS e _;Y xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!m{A#3+SrRIp101"X}" 0e(#!dԧAP{=t 9e!~[a?h>+= FE&EXL-\ŁofrQ~q~ZkaibIf~P%. 8z _,7f] d@CP~8c1Ɍ\\B͉ @V1 S-hTT$ eLmBJ` i@ dPVZWBRD`ɟ ,}WFT =D*(T }; xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!uLnzn`) 9 $ى C>@2ݑĐEB@A^XAӠlfOA`?ȭr4`y#"ZPDtcf.HC@73(8?D4$3?OXπ( ca=c/ u3 Ѯ2 v ϡ(Pa|1Ɍ\\B͉ ܌L \Lm ȢPQm`1 )%i&063 51t%m) Y!XgK<`=U*+C9=c'( (s6 ~jl?\#=6 xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!Pg9Ff V30d'2b`bDD`;PtGC y'bOzC? rB x}V({ LLhGZ i= Ē<c=K0\ȇqXn*$ ,D01""@2ݑĐEB@A^XAӠlfOA`?ȭr4`y#"ZQDtcf.HC@73(8?D4$3?OXπ( ca=c/ u3 Ѯ2 v !c(X[b2##3Ps"3?#7#S! S-S)SS o2ÈA9KMeĚ Paf>` 59 `E 222$KL`2Je`!'bŗ?eFOm0XY> xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!= ~9Ff V30d'2b`bDD`;PtGC y'bOzC? rB x}V({ LLhGZ i= Ē<c=K0\ȇqXn*$ ,D01<.q3v: :lPe Uf@*c06!%f>` 51@TeMx,PPʐ,3Oʈ*_9j?P?rP ' $))+,.p2 45Z79:<F>@Ae{C ;F&&\c s:@ |b@3X?]`!ԩf())~< Jkxcdd``gd``baV d,FYzP1n:&@ n;<xcdd``gd``baV d,FYzP1n:B@?b u f`h UXRY`7S?&,e`abM-VK-WMc<ObF\ Q\ ƕ0~; af Ra"z KKT,n`Bܤ\-pD@r']K? ׆12wp{-8@&YrAC  ;+KRs@2u(2t5 űg`!Q*IG xcdd`` @c112BYL%bpu&2rps_ݛg '.pXJ `PcdbR ,.IeHԡ"|b@3X?Bb`!K+14) θ;xcdd`` @c112BYL%bpu$d@9`,&FF(`Ts A?dba@=P5< %!@5 @_L ĺEXY@,a + LUN9( \pkB ?'i3vq1aiը$d~.}1< #46c@47$37X/\!(?71;!21pM`ZdpBzA`iiiy1402& j#@d|xxcdd`` @c112BYL%bpuL,+A7ݺJB K'[37yAD܈9M޻Μ{{}@3Mz]w3;m<*\sD;FOi!$1t4{^遼]ypR OSPvK~D!? g{(3 |h*SX~sC}o~u޼6X3PS18ɾ0 H`Žy` k kWZh?b~sT-jd [˗q3 =ܲ \{?*n2oSTm#TR_] *z͕ɱ .CeiD _c>ˆF3Yݜ~*<<{I^dtŨzF2Jay{Xwg0=7g"|[p_gɕӋHP)(Z?43 lc xVOKA}3nP"H z 5)R[I`K, hbLlzi ]ȩ ~zړg^fw.)1/f~fff_l%:x|B7eYN-m=,OqdQvWz Oo;q0T_uqzaB o=~=˟f:!0U_~_}Ce_o(Z}nߧc=]o/t^?|VQ+7vYUDn}vD W3Gu+0xPc"'*1gf! 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E3s}77* w:{V?YE΁t :ʘA@,Ki>Ɂ>/A'PTChU.WKUVpN>gKW 8(cp+gwӧ 5~#ً'xM;"%?dr|pH>OލѳO:x/wN)źx &`BQD_ @f\2raMCwœqӁp/\[ſӹ\//dsƟ\W)h?R#_n~.} Gg=}:FTx>'YΡր.xΩ]ct<.j i%8cRcZev;?_@vjv͌2>+f"|'9`VC ت8NE*Tl{AKǡb`4 g}h(חΆ vn;EL?L??жkclK-vYPHvmp`x0N71e`@F@2ݑĐEB@A^XAӠlfOA`?ȭr4Fā>8 NI{y_Hf&秕(&d)0\b @>grS!.`f`!ڵ@Ԏ9$w3&S!4˘00 ) 5icS- HBJ`yfmtt ?X?(RYz;AeFQS eE?w xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!}A#3+SrRIp101"X}" 0e(#!dԧAP{=t 9e!~[a?h>+= FE&EXL-\ŁofrQ~q~ZkaibIf~P%. 8z _,7f] d@CP~Üb<A.6[(S!TT$ eLmBJ` i@ dUjN ?X?(RYz;AUBQS e _;Y xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!m{A#3+SrRIp101"X}" 0e(#!dԧAP{=t 9e!~[a?h>+= FE&EXL-\ŁofrQ~q~ZkaibIf~P%. 8z _,7f] d@CP~8c1Ɍ\\B͉ @V1 S-hTT$ eLmBJ` i@ dPVZWBRD`ɟ ,}WFT =D*(T }; xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!uLnzn`) 9 $ى C>@2ݑĐEB@A^XAӠlfOA`?ȭr4`y#"ZPDtcf.HC@73(8?D4$3?OXπ( ca=c/ u3 Ѯ2 v ϡ(Pa|1Ɍ\\B͉ ܌L \Lm ȢPQm`1 )%i&063 51t%m) Y!XgK<`=U*+C9=c'( (s6 ~jl?\#=6 xp^RЀ3ÿ lHbP  LPÄ!1 4axĐ% y@( XyT0cH!Pg9Ff V30d'2b`bDD`;PtGC y'bOzC? rB x}V({ LLhGZ i= Ē<c=K0\ȇqXn*$ ,D01""@2ݑĐEB@A^XAӠlfOA`?ȭr4`y#"ZQDtcf.HC@73(8?D4$3?OXπ( ca=c/ u3 Ѯ2 v !c(X[b2##3Ps"3?#7#S! 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Vklad novho u iva je prokldn vzorovmi pYklady, kter u itel Yea se ~ky nebo pYklady, kter Yea ~ci sami (v etn vsledko). Clem hodiny je zskn zkladnch dovednost pro prci se zkladnmi vztahy pro aritmetickou posloupnost. Sou st materilu je pracovn list slou~c pro procvi en a samostatnou prci ~ko.hpPwPg   &/8  ` 33` Sf3f` 33g` f` www3PP` ZXdbmo` \ғ3y`Ӣ` 3f3ff` 3f3FKf` hk]wwwfܹ` ff>>\`Y{ff` R>&- {p_/̴>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>>  (     6Ќ  `}  XKlepnutm lze upravit styl pYedlohy nadpiso.- -  0   `  Klepnutm lze upravit styly pYedlohy textu. Druh roveH TYet roveH tvrt roveH Pt roveH,    `  0`  ^ `  >*  0  ^   @*  0  ^ `  @*  \A޽h ?Balic papr"` 3380___PPT10.v%r^w Vchoz nvrh_A    p (     <-_  > vodn loha   <L"`e,$D 0 j4 Rychlost aYen zvuku je pYi 0C 331 m/s S rostouc teplotou rovnomrn spojit roste PYi zvaen o 1C vzroste o 0,6 m/s Jak bude teplota pYi 5C ?-|  <G "`"%B,$ 0 `Ozna me vn rychlost v m/s pYi teplot (n  1)C01  & &  <"`~R,$D 0 4|PYi 0C v1 = 331 PYi 1C v2 = v1 + 0,6 = 331 + 1 . 0,6 PYi 2C v3 = v2 + 0,6 = v1 + 2 . 0,6 = 331 + 2 . 0,6 PYi 3C v4 = v3 + 0,6 = v1 + 3 . 0,6 = 331 + 3 . 0,6 PYi 4C v5 = v4 + 0,6 = v1 + 4 . 0,6 = 331 + 4 . 0,6 PYi 5C v6 = v5 + 0,6 = v1 + 5 . 0,6 = 331 + 5 . 0,6 Rychlost pYi teplot 5C je 331 + 3 = 334 m/s.?    #    $    #    %    KH  0޽h ? 33'77___PPT106.w%`!+D6' = @B DV6' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* +%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* +D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* +Y%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* +YD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* +YDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* Y~%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* Y~D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* Y~Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* ~%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* ~D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* ~D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* :%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* :D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* :Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* :o%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* :oD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* :oDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* o%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* oD' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* oDn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D b' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* ?%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* ?D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* ?+8+0+  +    $ (  $ $ 0W,U ,$ 0 rPosloupnost se nazv aritmetick prv tehdy, kdy~ existuje takov slo d, ~e pro ka~d len tto posloupnosti plat : an+1 = an + d. slo d se nazv: DIFERENCE posloupnostiJ  2,2 $ <r"`V * $ <^"`4,$ 0 0Hodnoty v1, & , v5 tvoY posloupnost. Ka~d len tto posloupnosti zskme tak, ~e k pYedchozmu lenu pYi tme slo 0,6. Rozdl po sob jdoucch leno je stejn ( konstantn) :0,6 Je to pYklad tzv. ARITMETICK posloupnosti.J   ^  $ 6  $ C A ?"?C 8 $D 0  $ <ț"`<,$ 0 vDosledek: Pro vaechna pYirozen sla plat: an+1  an = d.V<&  ,-^  $ 6H $ 0޽h ? 33QI___PPT10).y%þ+DU' = @B D' = @BA?%,( < +O%,( < +D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$DA' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*$D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*$D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* $%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* $D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* $D{' =%(D#' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* $%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* $D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* $++0+$  ++0+$  ++0+ $  +9 YQ( (  ( ( < j  9loha 1 ( <`"` T + b0Doka~te, ~e posloupnost ^ ( 6d ( C A ?"? R p ( 0$"`)y,$D 0 pan+1  an = 2( n + 1)  4  ( 2n  4) = 2n + 2  4  2n + 4 = 2 Rozdl dvou po sob jdoucch leno je 2 (konstantn). Tedy se jedn o aritmetickou posloupnost s diferenc 2. $  ( <D`j ,$ 0 @Cvi en^  ( 6  ( C A ?"? Z 8 $D 0B  ( <@"` ,$ 0 bRozhodnte, zda je dan posloupnost aritmetick?22  ( <P4 s =g ,$ 0 @Xeaen:^ ( 6 ( C A ?"? * 8 $@ 0^ ( 6 ( S A  ??"? p8 $@  0 ( 0,8"`,$  0 Y'Posloupnost je aritmetick s diferenc ((^ ( 6 ( C A  ?"?i8  $D  0 ( <"`n Aje aritmetick.H ( 0޽h ? 33**___PPT10*.{%@?+({D)' = @B Dq)' = @BA?%,( < +O%,( < +Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(@%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(@D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(@Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(@%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*(@D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*(@D ' =%(D ' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* (D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* (D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* (D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* (D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* (D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* (D' =%(DH' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* (%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* (D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* (D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*(D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*(++0+ (  ++0+ (  ++0+ ( ++0+( +7   , (  , , </ vNeche jsou n, r, s pYirozen sla. Pak v ka~d A.P. plat:<<j , C A   ?#" `?P  ^ , 6j , C A   ?#" `?/P=  |  , < `  Pozn. Prvn ze vztaho bude dokzn matematickou indukc v pracovnm listu. Druh vztah vychz z prvnho."je  , <l ,$ 0 9loha 2j  , <H% + ,$ 0 V A.P. je tYet len 5 a osm 15. Ur ete diferenci, prvn a sedmnct len.MM^  , 6((  , C A   ?#" `?  8  $D 0^ , 677 , C A   ?#" `?|  8  $D 0^ , 677 , C A ?#" `? G8 $D 0^ , 6(( , C A ?#" `? ~  8 $D 0^ , 6(( , C A ?#" `? | r 8 $D 0^ , 6++ , C A ?#" `? s8 $D  0^ , 6(( , C A ?"? U8 $D  0H , 0޽h ? 33Z)R)___PPT102).%+`HPD(' = @B DQ(' = @BA?%,( < +O%,( < +DN' =%(D' =%(D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* ,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* ,D' =A@BBBB0B%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* ,D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* ,Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<* ,%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<* ,D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* ,Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*,Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*,Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*,Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*,Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*,Dn' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =+4 8?\CB#ppt_xBCB#ppt_xB*Y3>B ppt_x<*,D' =+4 8?dCB1+#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*,+p+0+ ,  ++0+ , +> O G 0 (  0: 0 <T"`dt ,$ 0 ZPro sou et prvnch n leno A. 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RNDr. ODVRKO, O., DrSc.: Matematika pro gymnzia  posloupnosti a Yady, 1. vydn Praha Prometheus, spol. s r. o. 1995. 126 s. ISBN 80-85849-91-7 PETKOV, J. , MATEMATIKA  pYprava k maturit a pYijmacm zkouakm na vysok akoly, 1. vydn Praha Prometheus, spol. s r. o. 1998, 303 s. ISBN 80-7196-099-3BB,c  08X 8 \A޽h ?Balic papr"` 33___PPT10i.-@+D=' = @B +r 4'#~'       !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ     #!"$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|~     W c"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKMNOPQRSTUVXYZ[rdefghijklmnLbstuvwxy{|}~ Snmek 3 Snmek 4 Snmek 5 Snmek 6 Snmek 7 Snmek 8 Snmek 9 Pouit psma_forroforroY Kocmanablona nvrhuVloen servery OLENadpisy snmk