Need help with this GP question!

What is the 7th term of a GP if the difference between between it's 3rd term and 1st termis 18 and that between it's 4th and 2nd is 9?

What is the 7th term of a GP if the difference between between it's 3rd term and 1st termis 18 and that between it's 4th and 2nd is 9?

What have you tried?

The nth term of a GP is

ar^{n-1}

where a is the first term and r is the common ratio.

What have you tried?

The nth term of a GP is

ar^{n-1}

where a is the first term and r is the common ratio.

I've just tried to make these equations:-
a(r)^2 - a=18 ----(i)
ar - ar^3=9 ----(ii)
But I don't know what to do next 😓

I've just tried to make these equations:-
a(r)^2 - a=18 ----(i)
ar - ar^3=9 ----(ii)
But I don't know what to do next 😓

(i) can be rewritten as a(r^2-1)=18
(ii) can be rewritten as ar(1-r^2)=9 or -ar(r^2-1)=9

Can you see what the next step should be?

(i) can be rewritten as a(r^2-1)=18
(ii) can be rewritten as ar(1-r^2)=9 or -ar(r^2-1)=9

Can you see what the next step should be?

Okay, I'm trying.

Oh yess! I got it! Thanks a loads!! 😃