修5新课标人教A版高中数学教案

修5新课标人教A版高中数学教案

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2⚪§1.1.1ᳮᣴᣴ•ᦟ᪗"#$ᢈ&:()*+,-./012.3ᐵ5Ḅ6789ᳮḄᑁ;<ᐸ>?@A;CDᵨᳮ$-./ᑁ.2ᳮF-./ḄGHI⚪஺)J$@AKLMNᨵḄPQ"#R,ᐳU6Vᙠ+,-./0$ᐸ*.Ḅᐵ5,XYL()Z[\Y]^ᵫᱯaᑮcdeᳮfghᳮHIiᵨḄjklm஺no᝱3$qrZstLᙠ@JuvᢣYxᜐᳮ-./⚪ḄDz&{|stLᔠn\ᳮ67ᦪḄᦪuuv&{()-./ᦪஹᳮஹᔣḄᦪ"#Ḅὶ5ᩭᱥḄὶ5$>஺•ᦟᳮḄ672>?<ᐸHIiᵨ஺•ᦟ"G02ᐸ0Ḅ*.-./ᑨḄᦪ஺•ᦟ)JI.⚪Yᐭ᝞1.1T,AABCḄ0CB

3áᑖâ┦.-./2ã.-./G´nä᝞1.1-3,çAABCØ┦.-./É0AB×ḄëØCD,᪷Ñ+,.-.ᦪḄabÊᨵCD=asin@=6sin4ᑣsin/sinBbUᳮáôsinCsinBabM¯sin/sinBsinC¾1.1-3àuὃØᔲáÖᵨᐸ§@A>?³±ªᵫÕõ<01⚪M¯áÖὃ⇋ᵨᔣᩭẆV³⚪஺¾>A÷à)Am47,ᵫᔣḄùAáôAB=AC+CBᑣj-AB=j.AC+CBi:jAB=J-AC+j,CB|j||AB|cos¾90°-Aà=0+|J||CB|COS900-CcsinA=asinCᓽ.=.sinAsinCUᳮ)Cmáô&=—7|sinJsin6sinCÿAABCᐵᯠᡂ஺ᵫ!"☢ḄẆ&'()*+ᳮ-.+ᳮ/ᙠ123ᔜ567ᡠ9Ḅ-.Ḅ:;<ᓽ3_b_csin/sin5sin஺DᳮE+ᳮF1!-.+ᳮHIJ135Kᐸ9Ḅ-.ᡂ-:M:NᦪPJ1-ᦪᓽQᙠ-ᦪkSa=஻sinWb-ksinB,c-ksinCX2!u=_L.=q<_`q=,=▲,1-=qsin/1sinBsin஺sin/sinBsinCsinBsin/JsinC"ef-.+ᳮḄghiᵨP/জlfḄmnopᐸ15qᐸr5᝞4=uvXsmBঝlfḄmno5Kᐸ315Ḅ9qᐸrḄ-.x᝞sin/=Ssin3஺b1{ᙢlfḄ}~56qᐸrḄ56Ḅ'(iE஺DN⚪ᑖ᪆F

4N1.ᙠAABC3lfA=32.0°,3=81.8°,a=42,9cm,E஺E/᪷ᑁ6+ᳮC=180°-(A+B)=180°-(32.0°+81.8°)=66.2°X᪷-.+ᳮa^inB=42.9sin81.8°b=«80.1(c/n)XsinAsin32.0°᪷-.+ᳮ,asinC=42.9sin66.2°c=-------h74.1(52).sinAsin32.0n/9`E3ḄᩖSᵨᘤ஺N2.ᙠAA8C3lfa=20cm,6=28cm,A=40°,E(ᑮ1°,5ᑮ1cm)஺E/᪷-.+ᳮ,inA28sin40°sin3=a0.8999.20P00V3<180°,ᡠBR64°,ᡈBZ16°.প5z640,C=18Oo-(A+B)«18O°-(4Oo+64<))=76°,asinC20sin76()C~sinAsin400«30(CTO).(2)616°,C=180,,-(A+B)«180°-(40o+l160)=24°,asinC20sin24°«13(cm).sinAsin40°/nlfo56ᐸ315Ḅ9EᨵoEḄ஺HLᚪ¡¢5⚓¡¢1(1)ஹ2(1)⚪.D⊡ᐙ¡Flf§ABC3sin/:sin8:sinC=l:2:3,qa:6:c(¨ᫀ/1/2/3)W.ª«(ᵫ¬®«)ba+b+c(1)+ᳮḄ⊤°/±=A(A>0)sin/sinBsinCsin/+sin6+sinC^a=ksinA,b=ksinB,c=4sinC(A>0)(2)-.+ᳮḄᵨµ/জlfo6m15qᐸ7o5p1Xঝfo56ᐸ3159q¶15Ḅ9஺V.i¸¢10⚓D¡⚪L1A¹¢1(1)ஹ2(1)⚪஺

5º»¼ᣴ¾⚪/§1.1.2ᳮᣴ¿À/Áᣴ•ᦟÄ᪗fÆKᢈ/ÈÉÊ.+ᳮḄoË⊤°pÌIÊ.+ᳮḄᔣÎÏÐÑÒᵨÊ.+ᳮEÓo¿ghḄEÔ⚪஺'(KÏÐ/ᑭᵨᔣÎḄᦪÎÖÊ.+ᳮpᐸ×ÑØ'ÙÚÛÈÉᵨÊ.+ᳮEÓo¿ghḄEÔ⚪Ü᝱K_xÞ/ßàᙠÏ(áâᢣ*ᜐᳮEÔ⚪ḄWXØ'åᦪஹÊ.+ᳮஹᔣÎḄᦪÎÖF=CA—b,AB-c,Hc=a—8,|c|=c.c=(a-A)(a-=a-a+b-b-2a-b=|

667c2=a2+b2-2abcosC(?1.1-5)TᳮUa2+c2-2bccosAb2=3^+c2—2accosB2VWᑮ+YᳮZᳮ:\]^_`ab.Ḅcd2ᐸfg.ḄcḄhig.jklḄᜳ]ḄZḄnḄgo஺ᓽa2=bz+c~-2bccosAb2=a2+c2-2accosBc2=a2+b2-2abcosCqὃrst_ᨵv;6wḄ]xyᐸ_\;+!z{|;}ᔲᵫ\.!zb]ᵫz6ZᳮWᑮ+Yrh2+c2-a2cosA=-2^-2acᡝ+/b஺2cosC=2baᳮᳮ67Zᳮ4ᐸḄᵨrজ\]^Ḅ`g.4klḄᜳ]+!z{\.ঝ\]^Ḅ\ᩩ.+!zᐸk]஺qὃrᳮᢣz]\]^_\.cḄᐵZᳮᑣᢣzb\]^_\.cḄᐵ᝞aygᳮḄᐵᵫAABC_,C=90°,ᑣcosC=0,ᵫ¡ZᳮVᳮḄ¢ᳮVZᳮḄᱯ¤஺¤⚪ᑖ᪆¤1.ᙠAABC_a=2G,c=+,8=60°,!b4AপrVb2-a2+c2-2accosB=(2ᨵ)2+(76+6)2-2-26•(ª+>/2)cos45°=12+(«+¬2-46+1)=8:.b=25!A+ᑭᵨZᳮ¯+ᑭᵨᳮ:_b2+c2-a2_(2X/2)2+(A/6+X/2)2-(2A/3)2_1ফbrCSA==°2bc2x2±x²+&)2'Z.A=60°.

7´rVsinA=^sinB=^.sin45°,b2V2½+¾>24+1.4=3.8,26<2x1.8=3.6,.a

8Ð⚪r§1.1.3\]^ḄÔbáôᣴÐõör÷ᣴЕᦟù᪗jᢈ}rüýᙠ\]^Ḅg.4ᐸ_b.Ḅþ]\]^ᨵgᡈᡈᔜḄᑨ☢ᳮḄᵨ஺!ᑖ᪆$%&ᐺ()$*!+,ᔠ.ᵨ/ஹ12ᳮ,4ᦪ678ᨵᐵឋ<=>⚪஺@᝱BCDE/ஹ12ᳮ$ᙠ>⚪GHIḄᨵᐵឋ⚪஺n.ᣴ¡rt¢£Ẇx(1.ᙠAABCl$gha*,/,¦§Ḅ¨ᑖ᪆ᐜᵫsin6=24\=Baᑣ஺=180°—(/+8)

9..asinC^_c=——--A1.·A¸¹ᡈºG$R»a>6½]ᨵ¾¿ᨵᔲᑣ஺2.·A¸┦G$᝞ÃaN஺$ÅÆ¿ᨵ᝞Ãa<6,ÅÆ\ÈᑖW☢¨ᩭ¦§1Éa>bsin/,ᑣᨵi2Éa=6sin4,ᑣ¿ᨵ3Éacbsin/f,ᑣ஺Èa%ÌÍr`910⚓ÎÏÐÑᙠghḄij8ᐸljḄmG$¿ᨵ·A¸┦¾6sin//0[æ¹0AABCæ¹a?<஻+c2=/æ┦"AABCæ┦ÐÑ/æ┦èAABCæ┦72>52+32,ᓽ...AABCæ¹஺[ÔᚪÖ×2]1ᙠAABCl$ghsin/:sin8:sinC=l:2:3,ᑨÛAABCḄ஺2ghAABCëìᩩVacosí=$cosq,ᑨÛAABCḄ஺%ᫀ1AABCæ¹2AABCæῪᡈº(3.ᙠAABCl$1=60°,6=1,☢¸=.$"ñ,.ḄD2sinJ+sin5+sincᑖ᪆\ᑭᵨ☢ᳮS=1a6sinC=]acsin᜛=6csin4È8/2ᳮõõõa_b_c_a+b+csin/sin6sinCsin4+sin᜛+sinCᵫS=96csin/=ö÷c=2,

10ᑣ/=í2+02_2Z;CCOS/1=3,ᓽH=g,^_——þᜐ——==2sinJ+sin^+sincsinin.ᚪ(1)ᙠAABCa=55,8=16,"#$%&Ḅ☢)S=22o6,,%C(2)ᙠAABCᐸ$.ᑖ01aஹbஹc,"$%&Ḅ☢)S="ᓝ’,%C4(5ᫀ7(1)60°ᡈ120°;(2)45°)IV.>?@(1)ᙠAB$%&ḄC.Dᐸ.ḄE%F$%&>ᨵCFᡈFᡈHFIJ&;(2)$%&ᔜMNOḄᑨQRS;(3)$%&☢)QᳮḄVᵨ஺V.YZ[(1)ᙠAABCAB6=4,c=10,6=30°,\ᑨ]#$%&ḄFḄJ^஺(2)_xஹx+kx+2bc%$%&Ḅ$.d,eᦪxḄghj஺(3)ᙠAABC1=60°,a=l,6+c=2,ᑨ]AABCḄ&l஺(4)$%&ḄC.ᑖ013cm,5cm,noᡠᜳḄ%Ḅrs1Rt5——7x-6=0Ḅ᪷,xy$%&Ḅ☢)஺•{|_}ᣴY

11⚪7§2.2F$%&Vᵨ>ᣴNO7ᣴ•ᦟ᪗Bᢈ:ᵨsQᳮஹrsQᳮIBRSFᨵᐵḄe▭⚪FᵨḄᐵtRS7✌ᐜ£¤ᝯḄ_ᶧ§ᑭᙢª«1¬YḄ⁚¯°±²³஺ᐸ´@ᔠ¶Ḅe▭J^·ᵨ“¹º⚪ª»¼ὃ¾¿ÀÁÂ@ÃÄÅ✄Ç”Ḅᦟt᪷ÉᜧË⌕,¬DᦟᑁÎÏÐḄᑁᙠᐵѲÒ⚪_}ÓÔÕ>£Ö×ØஹÙ&ÚÛIÜÚÝÞßà¶áâFSNãFe▭⚪஺Eä2x᪵ḄÒæឋ⚪⌕èé¶êëÒæÖM¼ìª«¶»í⚪îïð〉òḄᢣôõJö᝱øùhÚ7ú»¶ᦪḄᐶü,îØýᦪḄVᵨùh;Õ>þÿᵨஹᦪ⊤⚪ᵨᓄᦪ⚪Ḅ•ᦟ▭⚪!"#$%ᡈ'%()*ᯠ,⌲%()*.ᑮ▭⚪Ḅ•ᦟ0᪷2⚪34ᦪ56*7#8•ᦟ9:I.;⚪<ᐭ1ஹ>?@ABC?@DEFGHIJᳮஹLIJᳮMNOPQMRST6Ḅ()U2ஹ>VWX᛻CZ[\],^D_`☢bcd$e'‘()"*ᡃP⍗ᑮkF$%⚪*“⍩nQNḄᨴpqᡃPᙢᳫtuᨵwxᕖU”ᙠ}~*ᜩᦻᨵᐜḄᘤ#ὅḄq*GEF᜻Ḅᑮk%ᝍḄᕖUᡃPB⍝*BḄqஹ*ᙠḼ¡wQ¢⌱¤Ḅ¥¦ᫀ*¨᝞QMᵨᐰ()ஹ«¬()Ḅ*ᡈ®¯)()n°Ḅ*±ᵫᙠ▭¥¦⚪Ḅ³´µ¶*·S¸n

12¹஺᝞»¼ᨵ½¾Ḅ¿À*nᵨᐰ()Ḅᩭ¥¦*ᡠM*ᨵS¸ᨵÃ▲ឋ஺GÆ☢ÇÈḄ⚪GᵨM`ḄᡠnḄ஺ÉᜩᡃPÊË@HIJᳮஹLIJᳮᙠÌÍḄ⌕ᵨ*✌ᐜẆt᝞Ñ¥¦q஺n.ÔᣴÖ;(1)▭¥¦⚪Ḅ9:$Ú⌕ᐙᑖݳᳮ⚪*HÞß#*à▭⚪áḄᩩãᡠäᣚᡂ()ḄBBḄçஹ)*è934ᦪ56ᩭä>é⚪ÔC(2)é1ஹ᝞*VAஹBᙠíḄî*⌕¥¦ïÀḄq*¥¦ὅᙠAḄ°ð*ᙠᡠᙠḄíîç⌱J$C,¥#ACḄqG55m,NBAC=51஺*NACB=75஺஺äAஹBḄq(øÞᑮ0.1m)1.2-1úûD1_AABC*᪷2BḄç)*ᵨR%Jᳮ¨ü〉þUúûD2_ᵨÿᳮ⚪◤⌕ᕖ஺ᑖ᪆⍝ᐵ!ᑮ#Ḅ%ᑮ&!ᑮ#Ḅ%'(Ḅ)*Ḅ+⚪,⚪-ᩩ/012ABḄ5,AC789,:᪷<=>Ḅᑁᳮ@A᧕᪷

132ஹ᝞},AஹBC%hᙠḄ5(&!ᑮ#),AஹBC%()*Ḅ஺ᑖ᪆1Ḅ\]⚪,ẆḄC&!ᑮ#Ḅ%'(Ḅ)*+⚪஺✌ᐜ◤⌕᪀⌼=>,ᡠ◤⌕CஹDC%஺᪷ḄCᑁb!FCḄ,ᑖFACBC,:ᑭᵨ¡Jᳮ!EFABḄ)*஺}1.2-2ὅ!ᙠ⌱C%CஹD,KCD=a,¥¦ᙠCஹDC%ᑖKNBCA¨¨,ZACD=p,ZCDB=,ZBDA=3ᙠAADCABDC,GᵨIJᳮKzf6tsin(/+Z>)஻sin(y+b)sin[180°-(/?+/+Ù,ᮣÛ᪷

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23S>=«-x41.4x38.7x0.6384^511.4(cm2)2Æ2ஹ᝞ù,ᙠµúûúü᛻ýnC⌕þOPQḄÿᦋ⌼ᡂᑁᑮḄᩩᑖ68m,88m,127m,Ḅ☢%&'()*+,ᑮ0.1cm20?2345678▭:⚪ᓄ=7⍝ᦪ@⚪Aᔩ)C3D⚪EFᓄGHḄIḄ:⚪JᑭᵨḄ☢%MIN஺ᵫ@CNQὁ2STUV@CNQWXYZ[\஺N3]a=68m,b=88m,c=127m,᪷bcdeᳮḄghc2a2-h2n+cosB=-----------2ca1272+682-882=---------------n0.75322x127x68sinB=Vl-0.75322®0.6578wᵨS=—acsinB2SJX68X127X0.6578Q2840.38(m2)2Q3Ḅ☢%&2840.38m2o3ஹᙠAABCI3ஹa2+b2sin2A+sin2Bপ——5—=-------;------c2sin2C(2)a2+b2+c2=2(bccosA+cacosB+abcosC)ᑖ᪆3&7⍝ᐵᐵឤMḄ:⚪MḄᱯὶᑮᵨdeᳮᩭ3*10᪷bdeᳮE]4===ksinAsinBsinCᯠk*0,ᡠ¤a2+b2A:2sin2A+A:2sin2B¦k2sin2Csin2A+sinB=sin2C*20᪷bcdeᳮḄgh,

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266ªᔲᵨCM:;⊤ÑÏÒy"]ÓCÔᳮ*ᦪᑡ⚗Ḅ,ÕÖᦪᑡḄ8⚗:;DE·☢Ḅᦪᑡঝ1C⚗°C⚗ḄÍᨵ°᪵ḄDuᐵ6⚗1·1.1123453IIIIÍ12345°MᦪḄC⚗°C⚗ḄͪᵨCM:;%=,ᩭ⊤ÑᐸDuᐵ6nᓽÛ⌕²ᵨ1,2,3…ÝÞ:;¤Ḅn,¢ª«ß@àᦪᑡuḄᔜ⚗Ãᔠ·¸ᐸᶹ1âjãᐸDuᐵ64.ᦪᑡḄ8⚗:;:᝞ᦪᑡ4Ḅn⚗a“n45Ḅᐵ6ª«ᵨCM:;ᩭ⊤Ñ,°M:;¢°MᦪᑡḄ8⚗:;.Bপ<ᡠᨵᦪᑡ¯(ᑏ@ᐸ8⚗:;1᝞·¸ᦪᑡট7ফCMᦪᑡḄ8⚗:;ᨵçCḄ1᝞ᦪᑡ1,0,1,0,1,0,…LḄ8⚗:;ª«,誫q=|cosS;r|.22বᦪᑡ8⚗:;Ḅêᵨজßᦪᑡ¤ABC⚗7ঝëìíᦪᔲàᦪᑡ¤ḄC⚗.ᦪᑡḄ8⚗:;ᐹᨵïsðñ1L⊤ÑᦪᑡḄò⚗1ó°Mᦪᑡ¤ᡠᨵᔜ⚗ḄC¾⊤Ñ.8⚗:;ô᧜CMᦪᑡ⚗⚗ᦪḄ3ᦪᐵ61öᦪᑡḄ8⚗:;1°Mᦪᑡ÷ø1Ýᐭ⚗ᦪ¢ªß@ᦪᑡḄ®C⚗.5.ᦪᑡ3ᦪḄᐵ6ᦪᑡª«Ìᡂ«᦮ᦪúN*ᡈLḄᨵ▲¹ú1,2,3,…1nüḄ3ᦪq=/஻1ÿᑮᜧḄᑡᦪ஺ᩭᦪᱏ᝞i=lஹ2ஹ3ஹ4…ᨵ!"#ᡃ%&'(ᑮ)ᦪᑡ*/ᐭfফஹf3,fভ…,fn,…6.ᦪᑡḄᑖ/01᪷2ᦪᑡ⚗ᦪḄ45ᑖ0ᨵ6ᦪᑡ0⚗ᦪᨵ▲Ḅᦪᑡ.9᝞ᦪᑡ1,2,3,4,5,6஺:ᨵ6ᦪᑡ;6ᦪᑡ0⚗ᦪ;▲Ḅᦪᑡ.9᝞ᦪᑡ1,2,3,4,5,6…:;6ᦪᑡ2᪷2ᦪᑡ⚗Ḅᜧᑖ0⌴=ᦪᑡ0>2⚗?@⚗ABCḄD⚗Ḅᦪᑡ஺⌴Eᦪᑡ0>2⚗?@⚗ABᜧCḄD⚗Ḅᦪᑡ஺Fᦪᦪᑡ0ᔜ⚗HIḄᦪᑡ஺᤮Kᦪᑡ0>2⚗?ᨵL⚗ᜧCḄD⚗ᨵL⚗CḄD⚗ḄᦪᑡMN0OPP33ḄQRᦪᑡSL:⌴=ᦪᑡ⌴EᦪᑡFᦪᦪᑡ᤮KᦪᑡTU9WXYOPP34-3591in.Oᚪ[\OPP36U[\3ஹ4ஹ5U⊡ᐙ[\Y:᪷2`☢ᦪᑡḄDb⚗ḄᑏdᦪᑡḄ)e⚗fg0

27246810(1)3,5,9,17,33,ফY1?y’Yব0,1,0,1,0,1,(4)1,3,3,5,5,7,7,9,9,•…(5)2,-6,12,-20,30,—42,2஻1+(T)"X0(1)a=2n+l(2)a=----------------(3)a=nn(2«-l)(2n+l)"2(4)ᦪᑡ1+0,2+1,3+0,4+1,5+0,6+1,7+0,8+1,.,i+(-ir••%=n+---(5)ᦪᑡ1X2,—2X3,3X4,—4X5,5X6,……,«„=(-l)+n(n+l)IV.OP⁚O\'`ᑁ0ᦪᑡᨵᐵ!᪷2e⚗fgᐸ⚗᪷2ᦪᑡḄDn⚗LᓫᦪᑡḄe⚗fg஺V.O¡¢£OPP38\⚪2.1ARḄ>1⚪•§¨©ªᣴ¡¬O⚪0§2.1ᦣᑡḄ¯°±ᓫ²³´ᣴO/µ0¶ᣴO(>2O•)•ᦟ¸᪗º»±ᢈ½0XᦪᑡḄ⌴¾fg¿À⌴¾fg±e⚗fgḄÁÂ᪷2ᦪᑡḄ⌴¾fgᑏdᦪᑡḄDb⚗ᳮXᦪᑡḄDn⚗ıÅḄᐵÆDZÈÉ0Êᔊᦪᑡº»ḄÌÍᳮXÎᵨḄÇ஺ÐÌ᝱Ò±ÓM0eP⁚OḄ\ÔᦪᩭÕÖ×ØÙᦪ\ḄᐶÛ஺•ᦟÜÝ᪷2ᦪᑡḄ⌴¾fgᑏdᦪᑡḄDb⚗•ᦟÞÝᳮX⌴¾fg±e⚗fgḄᐵÆ•ᦟÇI.O⚪ßᐭUà\áᐭYᦪᑡᨵᐵ!II.Wᣴ¶O

28ᦪᑡḄ⊤ãÈÉ1ஹe⚗fgÉ᝞ᦪᑡ4Ḅ>n⚗±äåæçḄᐵÆ&'ᵨ)fgᩭ⊤ã"#è)fgéêëè)ᦪᑡḄe⚗fg஺᝞ᦪᑡ0ì2,3,…Ḅe⚗fg᜜=▀+1ï6ðLL1…Ḅe⚗fgᓽ451,a=—(we27,)234Ḅe⚗fg*Q2ஹö÷ÉøùÖú᯿ᦪö÷ḄüÉüᦪᑡḄö.ᐹÔÈÉ:'⚗ᦪ஻þᙶ᪗Ḅ⚗ᓽᙶ᪗ᓽᙶ᪗ᙠ☢ᙶ᪗☢ᑮḄᦪᑡ,111]I---,'2'3'4'$%&ᦪᑡḄ'(ᡠ*ḄᦪᑡḄ'+,%-./Ḅ01ᙶ᪗2᦮ᦪᡠ456ᙠ78Ḅ9:;Ḅ&ᦪ<=>ᦪᑡḄ⚗ᦪ.@'(ABᙢDᑮᦪᑡḄ⚗E⚗ᦪᵫGᑮᜧIᓄ;IᓄḄKL.3ஹ⌴OPQRST6ᩭV>WXᨬZ[⌕ᵨ>^_.ᵨᐸᩭa=%5W▭c⚪.Befgᚮijk'lᐸmno/ᦪpqr.qr%stu;v:x1yfgᦪ4zᓽs94=1+3x2yfgᦪ5zᓽs2-5=2+3x3yfgᦪ6zᓽs3ߟ6=3+3x4yfgᦪ7zᓽs4—7=4+3x5yfgᦪ8zᓽs538=5+3x6yfgᦪ9zᓽs6ߟ9=6+3x7yfgᦪ10zᓽs7—10=7+3ᵨ⊤jfgᦪn⊤jyᦪᑣA*%yḄfgᦪ%ᦪᑡ="+31WnW7ᵨ%yḄfᦪᐸyᦪḄmno/ᦪᑡqrᵨ4%ᐵᣩᙢ%yḄfgᦪ.4ᡃḄ¡¢ᩭ£¤¥஺§¨p©ªD«'ᱏ,ᔲ[ᨵᐸ¯mnA°±²³p^l´mnqrµsuvyḄᐵtu;v%yḄfgᦪ6¶u%yfgᦪ£1஺ᓽq=4za=5=4+1=a,+1z4=6=5+1=a,+12¹«ºOsa=a_+1(2WnW7)nnx>u½ᡠᐵSᐸx1⚗ᓽAᐸ¯⚗Dᩭ4%ᐵ¾¿À⌕஺

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30(1)q=0,a=a+(2n—1)(n£N)Un+xn஺Zf(2)a=1,a-----(n£N)U]n+}a“+2(3)4=3,a஻+]=3a“2(neN).\প4=0,42=1F஺3=4,=9,a=16,a=(n—1)25n^3_a=3=1+2x3°,a=7=l+2x3l,4z=19=l+2x32,}23a=55=l+2x33,a=163=1+2x34,/.a=1+2,3,r1;45nIV.-ghi1⁚-k0lmnᑁp1.⌴CDEqᐸᵨU2.O⚗DEt᧜Ḅv⚗w⚗ᦪxyḄᐵ{F|⌴CDEt᧜Ḅv}~⚗^ᡈn⚗_xyḄᐵ{.V.-0⚪2஺1AḄ4ஹ6⚪ᣴ-⚪§2.2ᦪᑡᣴ-ᣴ-^1-g_•ᦟk᪗wᢈl\DḄᭆF;ᦪᑡvᦪᑡḄ▲ᩩ¢F᪷9£ᑨ¥;ᦪᑡvᦪᑡU¦§¨ᵨᦪᑡḄᔜ©⊤«Fᮣ®ᵨO⚗DE¯ᦪᑡḄ✌⚗ஹDஹ⚗ᦪஹᢣḄ⚗±²w³´ᔊᦪᑡḄ¶ᓫ¸¹±²AºᵨᦪᑡḄ»1\¼½⚪Ḅ±²஺¾¿᝱ÁwÂÃO±ᦪᑡᭆḄMNᭆÄFÅÆk¹Ḅஹᑖ᪆ÉᧇḄËFÌ᩽ÎÏFЯḄÑÒ஺•ᦟkÓÔᦪᑡḄᭆFᦪᑡḄO⚗DE஺•ᦟkÕÔᦪᑡḄឋוᦟk±²I.-⚪Øᐭ

314Ѿ᛻Û⁚-ᡃÝk0lᦪᑡḄ£qÞHᦪᑡA⊤«ḄᦪᑡḄß©³ᑡàஹO⚗DEஹ⌴CDEஹáâ.ãä³åæçḄèÁt᧜ᦪᑡḄᱯÔ஺n☢ᡃÝëã᪵äíî஺-1P41⚓Ḅ4;íîজ0,5,10,15,20,25,…ঝ48,53,58,63ঞ18,15.5,13,10.5,8,5.5(4)10072,10144,10216,10288,10366õçkÝö÷nFëëmÛø;ᦪᑡᨵúûᐳçᱯýþ•ᐳçᱯýå⚗ÿ⚗☢⚗Ḅᦪ(ᓽ)(⚗ḄᢣḄ⚗!⚗)ᡃ#$ᐹᨵ'(ᱯ*Ḅᦪᑡ,-ᦪᑡH..ᣴ011.ᦪᑡ2ᙢ᝞5ᦪᑡ678⚗9⚗⚗Ḅᦪ,'ᦪᑡ;<=ᦪᑡ'ᦪ;<=ᦪᑡḄ>(ᵨ-@"d”⊤E)஺(1).>dJᵫ⚗!⚗ᡠMNOPᵨ⚗!⚗ᩭR(2).TᦪᑡU4W,X4—a,i=d(n^ᐵḄᦪᡈ-@)na2,nGNᑣeᦪᑡᦪᑡdf>஺gὃᦪᑡজஹঝஹঞஹটḄn⚗>opᙠᔩs᝞5pᙠᑖuvws2.ᦪᑡḄn⚗>oa=«,+(«-V)dxᡈ+(஻௃nᦪᑡJ|ᵫᦪᑡ⚗}~ᐵNM.XᦪᑡUa,WḄ✌⚗>d,ᑣᐸJ|M"I=஻ᓽ="1+d48dᓽ=%+d=a1+2da—q=dᓽ%=+d=q+3d4ᵫeᦪᑡḄn⚗>oM+(஻l)dᦪᑡfᦪᑡᑣ⌕ᐸ✌⚗>d,RMᐸn⚗஺஻ᵫᐵMa=a+(m-l)Jm1ᓽ%=a-(m-l)Jmᑣa-a+(n-V)d=a-(m-l)J+(n-l)J=a-F(n-m)dn}fnm

32n—CLᓽᦪᑡḄ78n⚗>oa^a+(n-rn)dd=J~nmm-nx.1পRᦪᑡ8,5,2…Ḅ720⚗(2)-401Oᦪᑡ-5,-9,-13…Ḅ⚗s᝞57⚗sপᵫ4=8,d=5—8=2—5=—3n=20,M=8+(20—1)x(—3)=—49ফᵫq=—5,d=—9—(ߟ5)=TMᦪᑡn⚗>ofa=-5-4(71-1)nᵫ⚪⚪⌕¡ᔲpᙠ£᦮ᦪn,¥M-401=-5-4(“-1)ᡂ¨}Mn=100,ᓽ-401'ᦪᑡḄ7100⚗3ᦪᑡ2Ḅn⚗>oa“=p஻+4,ᐸ©pஹqᦪªw'ᦪᑡᔲJᦪᑡsX✌⚗>ᑖuvwsᑖ᪆ᵫᦪᑡḄJ|⌕ᑨJ4Oᦪᑡ⌕a“a,i(n>2)On^ᐵḄᦪ஺®na2¯(°ᦪᑡUfW©Ḅ±⚗a,%(n22))a=(/m+q)-p(஻-l)+q=pn+q-(pn-p+q)=஺fᦪn.♦.a”ᦪᑡ✌⚗q=p+q,>fp஺²জXp=0,ᑣ4>f0Ḅᦪᑡᓽfᦪᑡq,q,q,…ঝXp#0,³´fWᐵnḄµo6¶·⊤EᦪᑡḄᔜ¹ᙳᙠµ»ᦪy=px+qḄ¶·µ⚗Ḅᦪ>,¼½ᙠy¾Ḅ¿Àfq.ঞᦪᑡU%WfᦪᑡḄᐙ⌕ᩩÃᐸn⚗a“=pn+q(pஹqᦪ)Äᐸf73n⚗>o஺টᑨÅᦪᑡᔲᦪᑡḄÆÇᔲÈÉ3n⚗>o©Ḅ•m.1ᚪÌÍ1P45ÌÍ1ஹ2ஹ3ஹ4x⊡ᐙÌÍ1.(1)Rᦪᑡ3,7,11,……Ḅ74⚗710⚗.ᑖ᪆᪷ᡠ$ᦪᑡḄ3⚗RM✌⚗>ᑏÑÒᦪᑡḄn⚗>o6NRÑᡠR⚗.᪷⚪4=3,g7—3=4....ÒᦪᑡḄn⚗>of/=3+(஻-1)X4,ᓽ஺“=4஻-14=4*4—1=15,%(,=4X10-1=39.

33ÔᐵÕRÑn⚗>o.(2)Rᦪᑡ10,8,6,……Ḅ720⚗.᪷⚪4=10,4=8—10=—2..,.ÒᦪᑡḄn⚗>ofa“=10+(஻l)X(—2),ᓽa=~2n+U,.a=~2X20+12=n20-28.Ô⌕²⚪ÛÜḄÝឋßàឋ.(3)100Oᦪᑡ2,9,16,...Ḅ⚗s᝞57⚗s᝞5Oãᳮᵫ.ᑖ᪆⌕åᑨÅᦪᔲfæᦪᑡḄᐸ©⚗ᑣᐵÕ⌕ᔲpᙠ£᦮ᦪ஻ç¥Ma“'ᦪ.᪷⚪M4=2,d=9—2=7.eᦪᑡn⚗>ofa-2+(n-1)X7=7஻n-5.ê7஻-5=100,M஻=15,8100'ᦪᑡḄ715⚗.(4)-20Oᦪᑡ0,-3-,-7,……Ḅ⚗s᝞57⚗s᝞5O,2ãᳮᵫ.177ᵫ⚪a,=0,d=-3-.•.eᦪᑡḄn⚗>ofa=--n+-,2"22774777ê'஻+'=—20,M஻ìf'"+'=—20íᨵ£᦮ᦪᡠî20O'22722ᦪᑡḄ⚗.IV.1¯ðñnò⁚ôÍ✌ᐜ⌕ᳮö÷ᦪᑡḄJ|øᦪô⊤ùofa,i=d,(n22,nGN+).ᐸµ⌕úûüᦪᑡḄn⚗>o4=/+(஻l)d,þö÷ᐸÿᵨ.ᨬ⌕⌕ᐵ஺஻=0,“+(஻—)da“=pn+q(pஹq$%ᦪ)Ḅᳮ)*ᵨ.V.,-.,P452⚪2.2[A7]Ḅ91⚪•<=>?ᣴA,⚪§2.2BCᦪᑡᣴ,EFGᣴ,(92,H)

34•ᦟJK᪗MN*ᢈPQRBCS⚗ḄᭆVWXYZ[\]BCᦪᑡḄ^⚗_`ab_P^c^⚗_*defNBCᦪᑡḄឋhPᵨde*^⚗_Ḅᐵ)ijkl⚪஺cm*no^cBCᦪᑡḄdeḄᵨXYpqᦪrsᔠuvஹwᦪuvW^cBCᦪᑡ^⚗_Ḅxᵨpqnmuv஺yz᝱|*}~^cBCᦪᑡḄẆJQRBCᦪᑡ*ᦪᑡḄᑁᙠὶpqᱯ*Ḅᱥ஺•ᦟJBCᦪᑡḄஹ^⚗_ஹឋhḄᳮ)*ᵨ•ᦟJᮣᵨBCᦪᑡḄ`ឋh)ikᐵl⚪•ᦟJcmI.,⚪bᐭ✌ᐜ⁚,ᡠJ⌕ᑁ¢1.BCᦪᑡᙢ᝞¥¦ᦪᑡ9§⚗¨©⚗*ª«⚗ḄCB¬¦%ᦪᓽ4-a“_|=d,(n22,neN+),¯¦ᦪᑡ°±²BCᦪᑡ¯¦%ᦪ°±²BCᦪᑡḄ_C(%ᵨ³´"d”⊤¶).2.BCᦪᑡḄ^⚗_a=a,+(n-V)d=a”,+(஻▬¸ᡈa”=pn+q(pஹq$%ᦪ))n3.ᨵ»¼no½¾?¿_Cdজd=a“-a,_Iঝd="§Âঞa»"a'"d=n-1n-mn.ÃᣴG,l⚪᝞¥ᙠ஻*ÄSÅÆᐭ¦ᦪA,a,A,ᓃᡂBCᦪᑡᦪᑡÌÍAÎÏÐÍᩩÈÉa+hÑÒÓÒ§஻+:,ᑣAa=/?A2ᵫ×½½ØA="20aÙᡂBCᦪᑡ2Ú⊡ᐙÝ⚪ÞÝᙠBCᦪᑡ2SÓq+4=9,a=7,ß4%.4ᑖ᪆⌕ߦᦪᑡḄj⚗^%yã$ᐜßᐸ^⚗_⌕ß^⚗_åæM⍝¯¦ᦪᑡSḄèé⚗ê_CᡈὅM⍝¯¦ᦪᑡḄìí⚗(M⍝ìí⚗°M⍝_C)⚪SîïM⚗êð¦ñ⚗ᐵvᑮ¯ñ⚗ᐵᐭó……)•Wõ%ö$BCᦪᑡ஺Þ+஺6=஺4+஺3=9=஺3=9—஺4=9-7=2

35••d=Q4஺3=72=5/.a=a+(9—4)d=7+5*5=32/.%=2,%=32g4ÚÝÃ)Þ,P44ḄÝ2)ᶍ,P45[25ïMᦪᑡõ4ö$BCᦪᑡ(1)2a$=+Jᔲᡂ2a5=4+qᕖ(2)2q,=a,i+%“(஻>1)ᔲᡂᑮ"#(3),(஻>%>0)ᔲᡂ'ᑮ"#"#((ឋ*)ᙠ,-ᦪᑡ012m+n=p+q,ᑣ1a+a=a+amnpqᓽm+n=p+q=>a+a=a+a(m,n,p,qEN)mnpq89:জᵫa,“+a“=%,+/>?@m+n=p+q,®a+a=amnm+nAB(,-ᦪᑡCDEFᦪḄᐵIID.JᚪLM1.ᙠ,-ᦪᑡO஺“Q01RS᜜=101/2=311U✌⚗4CX-d2.ᙠ,-ᦪᑡOZ,Q012Ḅ=64=15Ua.IV.J\]"⁚J_M`abᑁd(1.A=fᔞ=a,A,஺,ᡂ,-ᦪᑡ22.ᙠ,-ᦪᑡ01m+n=p+q=>a+a=a+a(m,n,p,qFN)ninpqV.JklmJnP46p4ஹ5⚪stuvᣴkxJ⚪(§3.3,yzᑡḄpn⚗{ᣴJ|}(~ᣴJ(p1J\)

36ᦟ_᪗SCᢈ(,-ᦪᑡn⚗Xᐸᵨ,-ᦪᑡḄn⚗XDᓫḄCn⚗ᨵᐵḄ⚪C(9XḄ>XḄᵨ1_f¡¢ᱯ¤ᑮD¥1¦¢D¥ᑮᱯ¤Ḅ§¨©1{ª«ᡂ¬⚪1⚪ḄD¥9X>Ḅᦟ_1_f®¯§ᮣ±ឋC²▎ឋḄ´L1µ¶_fḄ§·¸.¹º᝱¼C½¾¿(9XḄ>1¶Àᦪ_0ḄÁy஺ᦟ_ÂÃ,-ᦪᑡn⚗XḄᳮஹ>Åᦟ_ÆÃᮣ±Åᵨ,-ᦪᑡn⚗XDᓫḄᨵᐵ⚪ᦟ_I.J⚪ᐭ“]ᦑÊ”(ÌÍÎᜧḄᦪ_Ð1ᜩᦻ_Ð1ÌÍᓝÔ\1ᨵDEὁÖ@`D⍝⚪1ὁÖØ(“ÀᙠÙᜧÐ@⍝⚪(1+2+…100=?”`ÜᑖÞ1ßàᜧÐᙠ(1+2=33+3=64+6=10…á?âãä\1ÌÍåæᩭèéØ:“1+2+3+…+100=5050஺ᦟÖ(“᝞ìá@éᫀḄÌÍèéØ(î1+100=1012+99=101-50+51=101,ᡠa101X50=5050”óôᦑÊõöᡃø((1)lᦪ_ùúḄÌÍ¢]ûᗐý¿þ1ᦢὃᡠᓫḄᱥឋḄ஺(2)!ᦑ#$%ᡃ'()*ᦪᑡ-n⚗Ḅ012⌕Ḅ456789:☢ᡃ'⌕<=Ḅ“᎔@AB”6஺II.GᣴIJ1.)*ᦪᑡḄ-஻⚗MN1Os“QROS-a+a+a-\------1-a_+aজn}23ninS„=a++a_+…+U+4ঝnn2জ+ঝO2S„=(a,+«„)+(a+a,-)+(4+a_)+•••+(4+«„)2n2a+a=a+=%+a_............tn2n2A2S„=«(«,+«„)ᵫcdOS“e஻ভ+ᓽ)hᡃ'ijQklᓝnopqrst⚪Ḅvwឋ.

372.)*ᦪᑡḄ-஻⚗MN2OS“=x+஻(஻ᵨrsMN⌕(S“z{ᐹᜓ~ᩩOn,a,axna“=1+(஻—l)dᐭMN1ᓽdOS,,ex+஻("cMN⌕(5“z{~ᩩO஻,<,d(ᨵoᨵᵨ)GJP49-50Ḅ1ஹ2ஹ3ᵫ3dḄᐵOᵫS”Ḅ¡i¢n=loS=q¤¢n—2o,a-S-S_,nnntm.Jᚪ§¨JP52§¨1ஹ2ஹ3ஹ4IV.Joª«⁚J¨®:ᑁ°O1.)*ᦪᑡḄ-஻⚗MN1Os"=22.)*ᦪᑡḄ-n⚗MN2OS“=஻±+V.J²³´JP52-53¨⚪Aµ2ஹ3⚪¶·¸pᣴ²¹J⚪O§2.3)*»ᑡḄḄn⚗4஺ᣴJ¼½OIᣴJ(¾2Jo)•ᦟÀ᪗ÂᢈOÄÅƧÇÈ)*ᦪᑡḄÉ⚗MN-஻⚗MN¤®)*ᦪᑡḄឋÊËÌᵨÍ'ÎAᐵt⚪¤Ìᑭᵨ)*ᦪᑡÉ⚗MN-v⚗ḄMNẆÑḄᨬÓ¤ÔÕ56OÖᔊMNØᵨḄÔÕ¤ÙÚ᝱ÜÝÓÞOÉÔᨵᐵᑁ°ᙠà▭âãḄØᵨäâåæÚçᦪèâã,

38éêëâãḄàᵨឋìíâ⌕ᗐÞïâãâãt⚪ËᦪᙢÎt⚪஺•ᦟ2ñƧÇÈ)*ᦪᑡḄ(MN•ᦟòñᮣãØᵨ(MNÎt⚪•ᦟÔÕI.J⚪íᐭ✌ᐜö÷:r⁚Jᡠø⌕ᑁ°O1.)*ᦪᑡḄ-஻⚗MN1Os“=஻(>+“")22.)*ᦪᑡḄ-஻⚗MN2OS“=x+஻5T”2n.GᣴIJúÑOJP51ḄúÑãû«üOýᙢ᝞ÿᦪᑡ{஺“},Ḅn⚗S”=+4஻+ᐸpஹqஹrᦪ,!"ᦪᑡ#$%&ᦪᑡᔩ(᝞*$+Ḅ✌⚗-.&ᑖ0$12(ᵫS=piv+qn+r,4ᵨ=q=᜛+q+rn729=S“S"T=(P஻2+qn+r)-[p(n-l')2+q(n-1')+r]=2pn-(p+q)d=a-a,T=[2pn-(p+q)]-[2p(n-1)-(/?+q)]=2pnC%&ᦪᑡḄD⚗.E2FS“+GHIᓄᡂELF2S=^n2+(a,-^)n,7dWO,$ᦪ⚗RḄHSEn[VWX]%&ᦪᑡ⚗Ḅᨬ[\⚪^_P51ḄV4XᶍbcFC%&ᦪᑡ⚗Ḅᨬ[\⚪ᨵefghF(1)ᑭᵨ᜜F74>0,d<0,n⚗ᨵᨬᜧ[.Iᵫ%NO,a“+]W0,r4nḄ[.7a“<0,d>0,n⚗ᨵᨬb[.Iᵫ4W0,r4nḄ[.(2)ᑭᵨS.FᵫS஺=,s+(a1-g)nᑭᵨHSuᦪvghr4ᨬ[9nḄ[

39m.^ᚪyz1.%&ᦪᑡ4⚗Ḅ$24,5⚗Ḅ-2⚗ḄḄ&$27,r"%&ᦪᑡḄ|⚗.E஺2.&ᦪᑡ}%~«=-15,.&d=3,rᦪᑡ}I~Ḅn⚗ᑭ5“Ḅᨬb[஺4IV.^9bc1.n⚗S,=஻஻2+w+ᐸpஹqஹrᦪpwO,#$%&ᦪᑡᦪᑡḄ✌⚗$q=p+q+r.&$d=2p[5,=a.=p+q+r,7஻=19|⚗.E$4=''ஹ73“-S“_|=_p+q,7஻2292.&ᦪᑡ⚗Ḅᨬ[\⚪ᨵefghF17a“>0,d<0,n⚗ᨵᨬᜧ[.Iᵫ0,a,,+]W0,r4nḄ[஺7%<0,d>0,n⚗ᨵᨬb[.Iᵫa“W0,4M20,r4nḄ[஺2ᵫSn-gnᑭᵨHSuᦪvghr4ᨬ[9nḄ[V.^^_P53z⚪[A]Ḅ5ஹ6⚪•ᣴ^⚪F§2.4%”ᦣᑡᣴ^Fᣴ^1^9•ᦟ¡᪗£¤-ᢈ¦F§¨%©ᦪᑡḄ#ª«ᳮX%©ᦪᑡḄ|⚗.E®¯«°±-ghF|°²VᳮX%©ᦪᑡḄᭆ´«µ¶·§¨%©ᦪᑡḄ|⚗.Eஹឋ¹¦ᙠᐹ¼Ḅ\⚪½᛻¿ÀᦪᑡḄ%©ᐵÂÃÄᦪÅƦǫ¼È%©ᦪᑡ-ᢣᦪuᦪḄᐵÂ஺½Ê᝱Ì-Í[ÎFᐙᑖÊÐᦪᑡ$Ñ᧜À²ÓÔḄƼÈᦪ$ᩭÖ×À²ÓÔ·Øᵨ×À²ÓÔḄᦪ$ÙÚ1ÛḄÜs$ÝÞßᕡḄÃÄzḄᐶâ஺•ᦟãä%©ᦪᑡḄ#ª|⚗.E•ᦟåäᮣÔØᵨ#ªE|⚗.EXçèᐵ\⚪

40•ᦟ°±I.^⚪¯ᐭêzF%&ᦪᑡḄ#ªFë—a,i=d,(nî2,ndN+)%&ᦪᑡ$ᱯðḄᦪᑡᙠÀ²ÓÔ◀ò%&ᦪᑡᡃôõÈ⍗ᑮø☢ᱯðḄᦪᑡ஺^_P41⚓Ḅ4VLFজ1,2,4,8,16,-^1111(2)1,—.—.—>—…24816ঞ1,20,202,203,20஺…ট10000x1.0198,10000xl.01982,10000x1.01983,10000x1.01984,10000xl.01985,……জஹঝஹঞஹট"#ᦪᑡᨵ'(ᐳᱯ+,ᐳᱯ-./0⚗2/⚗34⚗Ḅ6789#:ᦪ஺n.=ᣴ?@i.86ᦪᑡBᙢ᝞E#ᦪᑡ./0⚗2F⚗3GḄ4⚗Ḅ689#:ᦪH(I#ᦪᑡJKL86ᦪᑡ.I#:ᦪKL86ᦪᑡḄM6NM6O:ᵨQRq⊤T(q/஺)ᓽ-q(q¥0)an-\1°“./0⚗2”3“4⚗”^6_:ᦪ(q)Ea,,Fᡂ86ᦪᑡOqb-q(஻wN+,gW0)/2஺◚kl⚗a”஺0ngW0“஺,o0”pᦪᑡq᜜,sᡂ86ᦪᑡḄt⌕vᐙᑖᩩz.3Oq=l|q%s_:ᦪ஺2.86ᦪᑡḄO⚗M~1:a=a♦q"-'(«,0)nFᵫ86ᦪᑡḄᨵa—%qN2=a?q—(aஹq)q—aஹqNa=c^q=(ad)q=L4

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