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,求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,求q的值

人气：225 ℃　时间：2019-10-10 05:26:22

解答

若q=1,则S(n+1)=n+1,Sn=n,S(n+2)=n+2,此时S(n+1),Sn,S(n+2)不成等差数列所以q≠1,则Sn=a1*(1-q^n)/(1-q)a1*[1-q^(n+1)]/(1-q)+a1*[1-q^(n+2)]/(1-q)=2*a1*(1-q^n)/(1-q)[1-q^(n+1)]+[1-q^(n+2)]=2-2*q^nq^(n+1)+q^(n...