已知a1=3,且an=Sn-1+2n(n>=2),求an及Sn

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2025-03-06 23:26:11
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回答1:

解: an=Sn-1 +2^n=Sn-S(n-1)
2Sn-1+2^n+2^n=Sn+2^n
2(Sn-1+2^n)=Sn+2^n
则Sn+2^n为等比数列,S1+2^1=5
则Sn+2^n=5*2^(n-1)
Sn=3*2^(n-1)
当n>1时,an=Sn-Sn-1=3*2^(n-2),a1=3
答:当n>1时,an=Sn-Sn-1=3*2^(n-2),a1=3
Sn=3*2^(n-1)