Sn是公差不等于0的等差数列{an}的前n项和,若S5=40,且a1,a3,a7成等比数列,则an= _ .
问题描述:
Sn是公差不等于0的等差数列{an}的前n项和,若S5=40,且a1,a3,a7成等比数列,则an= ___ .
答
设等差数列的公差为:d
则有条件得;
5a1+
•d=405×(5-1) 2 (a1+2d)2=a1•(a1+6d)
∴
(舍),
a1=8 d=0
.
a1=4 d=2
∴an=a1+(n-1)d=2n+2.
故答案为:2n+2.