等比数列｛an｝中,前n项和7n满足S1,s3,S2成等差数列.求…①该数列的公比q.②群a1-a3＝3+求Sn

题目

等比数列｛an｝中,前n项和7n满足S1,s3,S2成等差数列.求…①该数列的公比q.②群a1-a3＝3+求Sn

答案

S1,s3,S2成等差数列,
∴2a1(1+q+q^2）=a1(1+1+q),
∴2q^2+q=0,q=-1/2.
②a1-a3=a1(1-1/4)=3,a1=4.
∴Sn=4[1-(-1/2)^n]/(1+1/2)=(8/3)[1-(-1/2)^n].