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?
$a_k(a_kr)(a_kr^2)=15625$ $\implies$ $a_k^3r^3=15625$ $\implies$ $a_kr=25$
$$\frac{25}{r}+25+25r=155$$