For an arithmetic-geometric series:

$$1+5\left(\frac{1}{2}\right)^{1}+9\left(\frac{1}{2}\right)^{2}+13\left(\frac{1}{2}\right)^{3}+\dots$$

(a) Find general term of the series.
(b) Sum the series upto $n$ terms.
(c) Sum the series upto infinite terms.