Question

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?

Answer 1

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