已知公差为d(d≠0)的等差数列{an}满足:a2,a4,a7成等比数列,若Sn是{an}的前n项和,则S10S5的值为(

2025-03-03 18:04:31
推荐回答(1个)
回答1:

∵{an}是等差数列 a2,a4,a7成等比数列,
∴a42=a2a7
即(a1+3d)2=(a1+d)(a1+6d)
整理得:a1d-3d2=0
∵d≠0
∴a1=3d
S10
S5
=
10(2a1+9d)
2
5(2a1+4d)
2
=
2a1+9d
a1+2d
=
15d
5d
=3
故选:C