Question

已知数列{an}是公差不为零的等差数列其前n项和,若a3是a1和a9的等比中项,且s5=15,

Answer 1

(a3)^2=a1*a9

(a1+2d)^2=a1*(a1+8d)

(a1)^2+4a1d+4d^2=(a1)^2+8a1d

4d^2=4a1d

a1=d

s5=(a1+a5)*5/2=5a3

5a3=15

a3=3

a3=a1+2d=3d

3d=3

d=1

a1=d=1

an=a1+(n-1)d

=1+n-1

=n

tn=1/1^2+1/2^2+1/3^2+1/4^2+.+1/n^2