Question:
The sum of a 15-term arithmetic series with first term 7  is $-210$.  What is the common difference?

Answer:
Let $d$ be the common difference.  Then the last term is $7 + (15-1)d = 7+14d$.  The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the sum of the series is \[\frac{7 + (7 + 14d)}{2} \cdot 15 = 15(7d + 7) = 105d + 105.\]We are told that this sum equals $-210$, so we have $105+105d = -210$, from which we find $d=\boxed{-3}$.

Note: $\boxed{3}$ is also accepted as an answer.