Hello,

I am struggling with the following question: 'The third, fifth and seventeenth terms of an A.P. are in geometric progression. Find the common ratio of the G.P.

I have done the following:

Let the third, fifth and seventeenth terms be x, y and z respectively. From which I have, from A.P:

x + 2d = y

x + 14d = z

y + 12d = z

Also from G.P:

xr = y

xr^2 = z

yr = z

xz = y^2

I have three unknowns and seven equations, which I think should be enough, but I seem to be going round in circles. I would very much appreciate it if someone could point me in the right direction and/or suggest another approach.

Thank you.