Question

已知Sn是等比数列an中的前n项和,S3.S9.S6成等差数列,求证a2.a8.a5成等差数列.

Answer 1

因为S3.S9.S6成等差数列

2S9=S3+S6

2a1(1-q^8)/(1-q)=a1(1-q^2)/(1-q)+a1(1-q^5)/(1-q)

2(1-q^8)=2-q^2-q^5

2q^8=q^2+q^5

2q^7=q+q^4

2a1q^7=a1q+a1q^4

2a8=a2+a5

所以a2.a8.a5成等差数列