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?_数学解答

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?

人气：184 ℃　时间：2019-10-14 02:03:47

解答

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