Question

设等比数列[an]的公比为q,前n项和为Sn,若S(n+1),Sn,S(n+2)成等差数列,则q的值?

Answer 1

q=1或者q=-2

Sn=(a1-a1*q^n)/(1-q)

Sn+1=(a1-a1*q^n+1)/(1-q)

Sn+2=(a1-a1*q^n+2)/(1-q)

(a1-a1*q^n)*2=a1-a1*q^(n+1)+a1-a1*q^(n+2)

2=q+q^2

q=1或者q=-2