Question:
An infinite geometric series has common ratio $-1/2$ and sum 45.  What is the first term of the series?

Answer:
Let the first term be $a$.  Because the sum of the series is 45, we have $45= a/[1-(-1/2)] = a/(3/2) = 2a/3$.  Therefore, $a=\boxed{\frac{135}{2}}$.