等差数列{an}的前n项和为Sn,且a3=5,S15=225.(1)数列{bn}满足:bn+1?bn=an(n∈N*),b 1=1,求数列{

2025-05-13 00:23:30
推荐回答(1个)
回答(1):

(1)设等差数列{an}的公差为d,由已知得:

a1+2d=5
15a1+
15×14
2
d=225

解得:a1=1,d=2
∴an=2n-1,
又bn=b1+(b2-b1)+(b3-b2)+…+(bn-bn-1)=1+a1+a2+…+an-1=1+
(n?1)(2n?2)
2
n2?2n+2

(2)cn2an+2n=22n?1+2n=
1
2
?4n+2n

Tnc1+c2+…+cn
1
2
(4+42+…+4n)+2(1+2+…+n)
=
2
3
(4n?1)+n2+n