设等差数列{an}的前n项和为Sn,已知a2=3,S5=25(1)求数列{an}的通项an(2)设数列{bn}满足bn=2an求数列{bn}的前n项和Tn.-数学

题目简介

设等差数列{an}的前n项和为Sn,已知a2=3,S5=25(1)求数列{an}的通项an(2)设数列{bn}满足bn=2an求数列{bn}的前n项和Tn.-数学

题目详情

设等差数列{an}的前n项和为Sn,已知a2=3,S5=25
(1)求数列{an}的通项an
(2)设数列{bn}满足bn=2an求数列{bn}的前n项和Tn
题型:解答题难度:中档来源:不详

答案

(1)设等差数列首项为a1公差为d
a2=a1+d=3
s5=5a1+10d=25

解得
a1=1
d=2

an=1+2(n-1)=2n-1

(2)bn=2an=22n-1
Tn=bn+bn+bn+…+bn
=21+23+25+…+22n-1=
21(4n-1)
4-1

=
2(4n-1)
3

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