Geometric progression exercise

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I have this statement:

Three numbers add up $155$ and its product is $15625$,

¿What are the terms?

I tried this:

Ok, three numbers add up $155$ is:

$a_k + a_k * r + a_k * r^2 = 155$

And, its product is 15625:

$a_k * a_k * r * a_k*r^2 = 15625$, i will divide by $r$ both sides.

$\frac{a_k}{r} * a_k * a_k * r = \frac{15625}{r}$

$(a_k)^3 = \frac{15625}{r}$

$a_k = 25* r^(\frac{1}{3})$

Then i replace in the first ecuacion of add up $155$:

$25* r^(\frac{1}{3}) + 25* r^(\frac{4}{3}) + 25 * r^(\frac{7}{3}) = 155$

Here, I did not know what to do, maybe I'm wrong at the beginning, but it's been trying for a while and I'm already confused, what's my mistake?

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$a_k(a_kr)(a_kr^2)=15625$ $\implies$ $a_k^3r^3=15625$ $\implies$ $a_kr=25$

$$\frac{25}{r}+25+25r=155$$