Question

如题已知a1=3 且 an=Sn-1 +2n（次方） 则 an=—— Sn=——

Answer 1

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)