### Instruction: The sum of a 15-term arithmetic series with first term 7  is $-210$.  What is the common difference?### Response: To solve this problem, I need to recall the formula for the sum of an arithmetic series.
An arithmetic series is a sequence of numbers where each term is obtained by adding a constant value, called the common difference, to the previous term.
The formula for the sum of an arithmetic series with first term a_1, common difference d, and n terms is S_n = n/2 (2a_1 + (n-1)d).
In this problem, I know that n = 15, a_1 = 7, and S_n = -210.
I need to find d.
I can plug these values into the formula and solve for d.
S_n = n/2 (2a_1 + (n-1)d)
-210 = 15/2 (2(7) + (15-1)d)
-210 = 15/2 (14 + 14d)
-210 = 105 + 105d
-315 = 105d
d = -315/105