Question

数列试题?SOS 急4．已知 an是各项为不同的正数的等差数列,lga1,lga2、lga4 成等差数列．又 bn=1/

Answer 1

1.

2lgA2=lgA1+lgA4

lg(A2)^2=lg(A1×A4)

(A2)^2=A1×A4

(A1+d)^2=A1(A1+3d)

(A1)^2+2A1d+d^2=(A1)^2+3A1d

又因为lgA1成立,所以A1>0

A1=d

An=nA1

Bn=1/A(2^n)=1/(2^n×A1)

1/A1是常数,所以{Bn}是以1/2A1为首项,1/2为公比的等比数列.

2.

B1+B2+B3

=1/2A1+1/4A1+1/8A1

=7/8A1=7/24

A1=3

d=3