已知等比数列{bn}是公比为q与数列{an}满足bn=3^an,(1)证明数列{an}是等差数列 (2)若b8=3,且数列{an}...
问题描述:
已知等比数列{bn}是公比为q与数列{an}满足bn=3^an,(1)证明数列{an}是等差数列 (2)若b8=3,且数列{an}...
已知等比数列{bn}是公比为q与数列{an}满足bn=3^an,(1)证明数列{an}是等差数列 (2)若b8=3,且数列{an}的前3项S3=39,求{an}的通项,(3)在(2)的条件下,求Tn=|a1|+|a2|+...+|an|
答
1.bn/b(n-1)=3[an-a(n-1)]=q
所以an-a(n-1)=log(3)q
2.a2=13
a8=1
d=-2
an=17-2n
3.n8 Tn=-[a1+.an]+2[a1+.+a8
=n^2-16n+128