Question

已知数列{an}是等比数列，a2=4，a3+2是a2和a4的等差中项，（1求数列{an}的通项公式

已知数列{an}是等比数列，a2=4，a3+2是a2和a4的等差中项，（1求数列{an}的通项公式（2）设bn=2log2的an-1次方，求数列{anbn}的前n项和

Answer 1

an = a1.q^(n-1)

a2=4
a1q=4 (1)

a3+2是a2和a4的等差中项

a2+a4 = 2(a3+2)
4+ 4q^2 = 2(4q +2)
q^2-2q=0
q=2

from (1)
a1=2
ie
an = 2^n

(2)
an= 2^n
bn=2log2^(a(n-1))

=2log2^(2^(n-1))
= 2^n .log2
cn = an.bn
=2^(2n).log2
c1+c2+...+cn
= (4/3)( 2^(2n -1) ) .log2