# Math Help - Problem Geometric progression

1. ## Problem Geometric progression

Write down the n-th therm of geometric progression if a1*a3=144 and a4-a2 = 15.

I don't know how to solve this...

2. Originally Posted by Nforce
Write down the n-th therm of geometric progression if a1*a3=144 and a4-a2 = 15.

I don't know how to solve this...
$a_1 \cdot a_3 = a_1 \cdot a_1 \cdot q^2 = 144$

and

$a_4 - a_2 = a_1 \cdot q^3 + a_1 \cdot q = 15$

Now, we have a system:
$a_1 \cdot a_1\cdot q^2 = 144$
$a_1 \cdot q^3 + a_1 \cdot q = 15$

Now, it is easy to solve this.

$a_1$ and $q$ determine the geometric progression.