Question

Three distinct numbers, $x,y,z$ form a geometric progression in that order, and the numbers $x+y,y+z,z+x$ form an arithmetic progression in that order. Find the common ratio of the geometric progression.

Answer 1

Let x be the first term of G.P. and y and z be the mth and nth terms respectively.

Then the common ratio is given by

$r=\frac{m-1}{n-1}=\frac{\log \frac{y}{x}}{log\frac{z}{x}}$