- 数学已知等差数列{an}的前n项和为Sn且满足a2=3,S6=3
- 已知等差数列{an}的前n项和为Sn且满足a2=3,S6=36.
⑴求数列{an}的通项公式
⑵若数列{bn}是等比数列且满足b1+b2=3,b4+b5=24.设数列{an×bn}的前n项和为Tn,求Tn.
- 已知等差数列{an}的前n项和为Sn且满足a2=3,S6=36.
⑴求数列{an}的通项公式
⑵若数列{bn}是等比数列且满足b1+b2=3,b4+b5=24.设数列{an×bn}的前n项和为Tn,求Tn.
(1) S6=(a1+a6)+(a2+a5)+(a3+a4)=3(a2+a5)=36--->a5=9
--->d=(a5-a2)/3=2--->a1=1--->an=2n-1
(2) (b4+b5)/(b1+b2)=q³=8--->q=2
b1+b2=b1(1+q)=3--->b1=1--->bn=2^(n-1)
Tn = 1+3*2+5*2²+7*2³+...+(2n-1)2^(n-1)
2Tn = 1*2+3*2²+5*2³+...+(2n-3)2^(n-1)+(2n-1)2^n
相减：Tn = (2n-1)2^n - 2[2+2²+2³+...+2^(n-1)] - 1
= (2n-1)2^n - 2(2^n-2) - 1
= (2n-3)2^n + 3