Geometric Progression (1 Viewer)

[Pyrobooby]

If in a geometric sequence the sum of the second and third terms is 20 and the sum of the fourth and fifth terms is 320, find the common ratio and the first term. Assume that the common ratio is positive.

Couchman 3U Book 1 Ex. 14.8 Q18

I tried:
ar+a(r^2)=20 ----1
a(r^3)+a(r^4)=320----2
but got nowhere. I'm pretty sure the solution is something simple that I probably missed, but thank you in advance.

 

[deterministic]

Factorising gives
a(r+r^2)=20...(1)
ar^2(r+r^2)=320....(2)
(2)/(1)=>
r^2=16
r=4 or -4
if r=4 then a=1
if r=-4 then a=5/3

 

[Pyrobooby]

Thank you for the fast reply.

I want to slap myself when I don't see things like this -_-