设等比数列｛an｝的前n项和是Sn,若S6/S3=3则S9/S6等于几答案是7/3希望

Question

设等比数列｛an｝的前n项和是Sn,若S6/S3=3则S9/S6等于几
答案是7/3
希望

Answer 1

S6=a1(q^6-1)/(q-1)
S3=a1(q^3-1)/(q-1)
S6/S3=(q^6-1)/(q^3-1)=3
(q^3+1)(q^3-1)/(q^3-1)=3
q^3+1=3
q^3=2
S9=a1(q^9-1)/(q-1)
所以S9/S6=(q^9-1)/(q^6-1)
=(q^3-1)(q^6+q^3+1)/(q^3+1)(q^3-1)
=(q^6+q^3+1)/(q^3+1)
=(4+2+1)/(2+1)
=7/3