Question

高一数学数列题

已知d>的等差数列 an前n项和为Sn A3*A4=117,A2+A5=22
1.求an
2.若bn是等差数列 bn=Sn/(n+c),求非0常数c

Answer 1

a2=a1+d
a3=a1+2d
a4=a1+3d
a5=a1+4d
所以（a1+2d）*(a1+3d)=117
(a1+d)+(a1+4d)=22
联立得：a1=1;d=4
所以an=1+4(n-1)=4n-3
Sn=(2n-1)*n

Answer 2

a2+a5=a3+a4
结合A3*A4=117；a3+a4=22可求出a3，a4，继而求出a1和d
再求an

Answer 3

设a3=x
x(x+d)=117
x-d+x+2d=22
解得：x=9或13
所以d=4或-4
因为d>0
所以d=4,x=9
所以a1=9-2*4
=1
所以an=4n-3

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