【課件】第四章數(shù)列求通項(xiàng)公式專(zhuān)題課件高二下學(xué)期數(shù)學(xué)人教A版（2019）選擇性必修第二冊(cè)

第四章數(shù)列專(zhuān)題數(shù)列的求通項(xiàng)的基本方法數(shù)列求通項(xiàng)公式10種方法1.作差法2.作商法3.累加法4.累乘法構(gòu)造輔助數(shù)列法5.待定系數(shù)法7.取倒數(shù)法6.同除以指數(shù)法8.周期型數(shù)列例1.解：求數(shù)列通項(xiàng)常用方法—1.作差法求數(shù)列通項(xiàng)常用方法—1.作差法解：①②①－②得，變式2.求數(shù)列通項(xiàng)常用方法—1.作差法解：①②①－②，得變式2.解法2：小結(jié)：題目中有Sn求an，必用作差法.誰(shuí)簡(jiǎn)單化掉誰(shuí)變式3.(全國(guó)II，2015)解：例2.求數(shù)列通項(xiàng)常用方法—2.作商法解：①②①÷②得，變式.解：變式.求數(shù)列通項(xiàng)常用方法—2.作商法例3.求數(shù)列通項(xiàng)常用方法—3.累加法解：變式1.求數(shù)列通項(xiàng)常用方法—3.累加法解：變式2.求數(shù)列通項(xiàng)常用方法—3.累加法解：例4.求數(shù)列通項(xiàng)常用方法—4.累乘法解：變式1.求數(shù)列通項(xiàng)常用方法—4.累乘法解：變式2.設(shè){an}是首項(xiàng)為1的正數(shù)數(shù)列,且

(n+1)a2n+1–na2n+an+1an=0(n∈N﹡),求an.解:（n+1)a2n+1–na2n+an+1an=0分解因式為

(an+1+an)[(n+1)an+1–nan]=0.

∵an>0

,

∴

an+1+an≠0.

∴(n+1)an+1–nan=0，即解:設(shè)an+1+r=3(an+r),則

an+1=3an+2r.由已知

an+1=3an+4,得2r=4,即

r=2.

∴

an+1+2=3(an+2),例5.已知數(shù)列{an},an+1=3an+4,且a1=1.

證明數(shù)列

{an+2}是等比數(shù)列，并求出an.∴數(shù)列{bn}是首項(xiàng)為b1=a1+2=3,公比為3的等比數(shù)列.∴

bn=an+2=3×3n-1

∴

an=3n+1-2.例5.已知數(shù)列{an},an+1=3an+4,且a1=1.求an.求數(shù)列通項(xiàng)常用方法—5.待定系數(shù)法解：∴數(shù)列是以為首項(xiàng),以2為公差的等差數(shù)列.

例6.求數(shù)列通項(xiàng)常用方法—6.取倒數(shù)法變式1.考點(diǎn)四求數(shù)列通項(xiàng)常用方法—7.取倒數(shù)法解：變式2.各式相加得：解：考點(diǎn)四求數(shù)列通項(xiàng)常用方法—7.取倒數(shù)法例7.考點(diǎn)四求數(shù)列通項(xiàng)常用方法—7.同除以指數(shù)法解：變式.考點(diǎn)四求數(shù)列通項(xiàng)常用方法—7.同除以指數(shù)法解：例10.考點(diǎn)四求數(shù)列通項(xiàng)常用方法—8.周期型數(shù)列解：變式1.解：考點(diǎn)四求數(shù)列通項(xiàng)常用方法—8.周期型數(shù)列變式2.解：數(shù)列求通項(xiàng)公式10種方法