What is the sum of the finite arithmetic series?
(-15)+0+15+30++195
a. 1,355
b. 1,350
c. 1,335
d. 1,000

The underlying arithmetic progression is

-15, 0, 15, 30, ...

starting with and with a common difference of between terms. Recursively, this sequence is given by

So we have

and so on, so that the explicit rule for the sequence is

for .

The series consists of 15 terms, since

So we have

and the answer would be B.