Infinite series convergence value problem 
Is it possible to find the convergent value of the series:  $\sum\limits_{x=0}^{\infty}(x+3) \cdot a^x $ where $a$ is a constant less than 1?

I thought about expanding:
$\sum\limits_{x=0}^{\infty}(x+3) \cdot a^x =\sum\limits_{x=0}^{\infty}x \cdot a^x + 3 \sum\limits_{x=0}^{\infty} a^x$
and the second term is just $\cfrac{3}{1-a}$, but I don't know what to do with the first term.  Is there a general method to solve these types of problems?  I that there are many types of convergent tests but not sure about methods to actually find convergent value.  Thanks in advance.

$$\sum_{x=0}^{\infty} a^x = \dfrac1{1-a}$$
$$\sum_{x=0}^{\infty} xa^x = \sum_{x=0}^{\infty} a (xa^{x-1}) = \sum_{x=0}^{\infty} a\dfrac{d}{da}\left(a^x\right) = a\dfrac{d}{da}\left(\sum_{x=0}^{\infty} a^x\right) = a \dfrac{d}{da}\left(\dfrac1{1-a}\right) = \dfrac{a}{(1-a)^2}$$
