设等比数列｛an｝的前N项和为Sn,若S10：S5=1：2
问题描述：
设等比数列｛an｝的前N项和为Sn,若S10：S5=1：2
S15：S5为多少
答
S10：S5
=[a1(1-q^10)/(1-q)]：[a1(1-q^5)/(1-q)]
=(1-q^5)(1-q^5)/(1-q^5)
=1+q^5=1:2
q^5=-1/2
S10：S5
=[a1(1-q^15)/(1-q)]：[a1(1-q^5)/(1-q)]
=(1-q^5)(1+q^5+q^10)/(1-q^5)
=1+q^5+q^10
=1-1/2+1/4
=3:4