I have an exercise, which says:
Determine 4 numbers in geometric progression, such that the first 2 numbers add 9, and the last two numbers add up to 36.
I know all the formulas and I tried everything, but I can not get the result.
I thought that by making a system of equations like:
$ a_1 + a_1 * r = 9$
$a_1 * r^2 + a_1 * r^3 = 36$
Here I could not do more, how is it done?
Or my approach is wrong?
You have s good start. The ratio of the equations gives $r^2=4$ so $r=\pm 2$. Divide the first equation by $1+r$ to get $a_1$. The numbers are -9,18,-36,72 or 3,6,12,24.