Question

设｛An｝为等差数列,公差d为正数,已知a2+a3+a4=15 又（a3-1）的平方=a2*a4

Answer 1

1.｛An｝为等差数列,所以2a3=a2+a4

a2+a3+a4=15=3a3 a3=5

(5-1)^2=16=(5-d)(5+d)

d=3 (-3舍掉)

所以a1=5-2d=-1 d=3

2.

an=a1+(n-1)*d=3n-4

Sn=3-4+6-4+9-4+...+3n-4

=3*(1+2+3+...n)-4n

=3*n*(n+1)/2-4n

=3/2*n^2-5/2*n