设等差数列{an}的前n项和为Sn,已知a3=5,S3=9.(Ⅰ)求首项a1和公差d的值;(Ⅱ)若Sn=100,求n的值

2025-06-27 10:04:58
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回答1:

(Ⅰ)∵等差数列{an}中,a3=5,S3=9,

a1+2d=5
3a1+
3×2
2
d=9

解得a1=1,d=2,
(Ⅱ)∵a1=1,d=2,
Sn=n+
n(n?1)
2
×2
=n2=100,
∴n=10.