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...
$\displaystyle a_1 \cdot a_3 = a_1 \cdot a_1 \cdot q^2 = 144$
and
$\displaystyle a_4 - a_2 = a_1 \cdot q^3 + a_1 \cdot q = 15$
Now, we have a system:
$\displaystyle a_1 \cdot a_1\cdot q^2 = 144$
$\displaystyle a_1 \cdot q^3 + a_1 \cdot q = 15$
Now, it is easy to solve this.
$\displaystyle a_1$ and $\displaystyle q$ determine the geometric progression.