Geometric series with modified terms

I am looking for a way to sum some numbers. I understand that if I want to sum pi, I can use the geometric series:

$\sum\limits_{i=0}^N p^{i} = \frac{1-p^{N+1}}{1-p}$

But can anyone help me with what to do when I need:

$\sum\limits_{i=0}^N p^{i} q^{ti}$

where t is just a constant.

Thank you in advance of any help!
 Let : $P = p.q^{t}$