作业帮设等比数列[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?
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![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?](/uploads/image/z/3970671-15-1.jpg?t=%E8%AE%BE%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%5Ban%5D%E7%9A%84%E5%85%AC%E6%AF%94%E4%B8%BAq%2C%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E8%8B%A5S%28n%2B1%29%2CSn%2CS%28n%2B2%29%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E5%88%99q%E7%9A%84%E5%80%BC%3F)
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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?
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?
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?
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
q=-2