Application of geometric progression

Question

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?

Hint: multiply the first equation by $,r^2,$ and see what you get. — dxiv, Apr 05 '18 at 22:22

score 2 · Answer 1 · answered Apr 05 '18 at 22:22

2

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.

answered Apr 05 '18 at 22:22

J.G.

115,835

Thanks J.G for your answer – ESCM Apr 05 '18 at 22:28

Application of geometric progression

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