Question

记sn为等比数列an的前n项和,若a1=1,s3=3/4

已知{an}是等比数列(1)若a1= -1,q=1,求前n项和Sn (2)若a1=1,S3=3/4,求公比q

Answer 1

a(n)=aq^(n-1),
(1) a(n)=-1,
s(n)=-n.

(2)a(n)=q^(n-1),
3/4 = s(3) = [1-q^3]/(1-q) = 1+q+q^2,

0 = 1/4 + q + q^2 = (q+1/2)^2,
q=-1/2