Question

已知等比数列{an}的前5项和为48,前10项和为60,则前15项和的值为?

Answer 1

设这个等比数列的首项为a1,公比为q,前n项和为Sn,则有

S5=a1(1-q^5)/(1-q)=48

S10=a1(1-q^10)/(1-q)=60

因为48/5≠60/10,所以q≠1

因此q^5=1/4,a1/(1-q)=64

S15=a1(1-q^15)/(1-q)=63