Create a series that answers the following criteria
You have
$$\begin{aligned} \sum_{n=1}^{\infty}(-1)^{n+1} a_{n} &= \sum_{n=1}^{\infty}(-1)^{n+1} a_0 q^n\\ &=-a_0 \sum_{n=1}^{\infty}(-q)^n\\ &=-a_0 \left(\sum_{n=0}^{\infty}(-q)^n - 1\right)\\ &= -a_0 \left(\frac{1}{1+q} - 1\right) = \frac{a_0 q}{1+q} \end{aligned}$$
Now, you need to have $\frac{a_0 q}{1+q}=4$ and $0 \lt q \lt 1$ as $\{a_n\}$ is decreasing.
$a_0 = 12$ and $q = \frac{1}{2}$ will do the job.