Finding the constant $c$ for the pmf $f(x)=c^{x-10}$, where $x=12,14,\ldots,32$

Question

I'm stuck with the following question and I don't know how to proceed.

Given PMF of a random variable of discrete type

$$f(x)= c^{x-10}$$

where $x= 12, 14, \ldots,32$, find constant $c$.

Now, this is what I know and what i've tried: the sum of the constant $c$ must equal to $1$. However, after laying out I end up with a long algebra equation I don't know how to solve.

i.e.

$$c^2+c^4+c^6...c^{22} = 1$$

Any help is greatly appreciated

Ps. Sorry for the formatting, I am new and I'm still figuring out my way around the formatting parameters.

Answer 1

Hint: the sum of $n$ terms of geometric progression: $S_n=\frac{b_1(q^n-1)}{q-1}$, where $b_1=c^2$, $q=c^2$, $n=11$.