数列前N项和比值问题等比数列{an}的前n项和是Sn若S6比S3=3,则S9比S6等于多少

Question

数列前N项和比值问题
等比数列{an}的前n项和是Sn
若S6比S3=3,则S9比S6等于多少

Answer 1

设公比为q
S6=a1(1-q^6)/(1-q)
S3=a1(1-q^3)/(1-q)
S6/S3=(1-q^3)(1+q^3)/(1-q^3)=1+q^3=3
所以q^3=2
S9=a1(1-q^9)/(1-q)
故S9/S6=(1-q^9)/(1-q^6)=(1-2^3)/(1-2^2)=7/3
希望可以帮到你,望采纳,谢谢.