Question

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

Answer 1

s1＝a1，s2＝a1+a1*q，s3＝a1+a1*q+a1*q*q

由S1，s3，S2成等差数列得

a1+a1+a1*q＝2（a1+a1*q+a1*q*q）得q＝－1/2

a1-a3＝3得a1＝4

所以Sn＝a1(1-q^n)/(1-q)＝4*[1－（－1/2）^n]/(1+1/2)=8/3*[1－（－1/2）^n]