### Instruction: The sum of a 15-term arithmetic series with first term 7  is $-210$.  What is the common difference?### Response: I recall that the sum of an arithmetic series with n terms, first term a, and common difference d is given by the formula S_n = n/2 (2a + (n-1)d).
In this problem, I know n = 15, a = 7, and S_n = -210, so I can substitute these values into the formula and solve for d.
I get -210 = 15/2 (2*7 + 14d), which simplifies to -210 = 105 + 105d.
Subtracting 105 from both sides, I get -315 = 105d.
Dividing both sides by 105, I get d = -3.
So the common difference is -3.