题目
设Sn为等差数列的{an}的前n项和,已知s3,s4的等比中项是S5,s3,s4的等差中项是1,求an?
提问时间：2020-10-12
答案
S5^2 = S3*S4
(S3+S4)/2 = 1=>S3+S4 = 2
S3 = a1+a1+d + a1 + 2d = 3a1 + 3d
S4 = 4a1 + 7d
S5 = 5a1 + 12d
S3 + S4 = 7a1 + 10 d = 2 => d = 1/5 - 7/10 a1
(3a1+3d)(4a1+7d) = (5a1+12d)^2
you can solve a1 and d with two equations
(S3+S4)/2 = 1=>S3+S4 = 2
S3 = a1+a1+d + a1 + 2d = 3a1 + 3d
S4 = 4a1 + 7d
S5 = 5a1 + 12d
S3 + S4 = 7a1 + 10 d = 2 => d = 1/5 - 7/10 a1
(3a1+3d)(4a1+7d) = (5a1+12d)^2
you can solve a1 and d with two equations
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