Question

设{an}是公比大于1的等比数列,Sn,为数列{an}的前n项和,已知S3=7,且a1+3,3a2,a3+4构成等差数列

Answer 1

(a1)+3,3(a2),(a3)+4构成等差数列,

故2*3(a2)=(a1)+(a3)+4

同时S3=(a1)+(a2)+(a3)=7

{an}是公比大于1的等比数列,

设公比为q,

则（a1)*q^2=(a2)*q=(a3)

联立得(a1)=1,

q=2

故(an)=2^(n-1)