Question

正项等比数列｛An}满足A2*A4=1,S3=13,Bn=㏒3 An,则数列{Bn}的前10项的和是多少

Answer 1

A2*A4=A1*q * A1*q^3=1 ==>A1^2*q^4=1

S3=A1+A2+A3=A1*(1+q+q^2)=13

==> A1=9 q= 1/3

An=A1*q^(n-1)=9*(1/3)^(n-1)=3^2*3^(1-n)=3^(3-n)

Bn=log 3 An=3-n

Tn=3n-n(n+1)/2

T10=3*10-10*11/2=-25