What is the sum of the arithmetic sequence 151, 137, 123, ... if there are 26 terms?

A. - 676

B.-650

C.-624

D.-598

First term: a1 = 151

common difference: d = - 14 (we decrease by 14 each time, eg, 151-14 = 137)

nth term of this arithmetic sequence is ...

an = a1+d (n-1)

an = 151 + (-14) (n-1)

an = 151-14n+14

an = - 14n+165

This will be used in the formula below

Sn = n * (a1+an) / 2

Sn = n * (151 + (-14n+165)) / 2

S26 = 26 * (151 + (-14*26+165)) / 2 ... replace every n with 26

S26 = - 624

The final answer here is choice C) - 624