Question

等比数列a+log(2)3,a+log(4)3,a+log(8)3

Answer 1

[a+log(4)3]^2=[a+log(2)3][a+log(8)3]

[a+lg3/2lg2]^2=[a+lg3/lg2][a+lg3/3lg2]

令x=lg3/(6lg2)

则(a+3x)^2=(a+6x)(a+2x)

a^2+6ax+9x^2=a^2+8ax+12x^2

-3x^2=2ax

显然x不等于0

所以a=-3x/2

所以q=(a+3x)/(a+6x)=(-3x/2+3x)/(-3x/2+6x)=1/3