设Sn是公差不为0的等差数列{an}的前n项和,且S1,S2,S4成等比数列.(1)求a5a7的值;(2)若a5=3,求an

2025-06-27 21:50:27
推荐回答(1个)
回答1:

(1)设Sn的公差为d,
∵S1,S2,S4成等比,
∴,S22=S1S4
即(2a1+d)2=a1(4a1+6d),化简得d2=2a1d,
又d≠0,
∴d=2a1
0≤x≤3

a5
a7
a1+4d
a1+6d
9d
13d
9
13

(2)∵a5=a1+4d=9a1=3,
a1
1
3
,d=
2
3

ana1+(n?1)d=
2n?1
3

Sn
a1+an
2
n
=
n2
3