# What is the sum of a 12–term arithmetic sequence where the last term is 13 and the common difference is –10?

Sep 30, 2016

Let's first determine the first term.

${t}_{n} = a + \left(n - 1\right) d$

$13 = a + \left(12 - 1\right) - 10$

$13 = a - 110$

$123 = a$

We now apply the formula ${s}_{n} = \frac{n}{2} \left({t}_{1} + {t}_{n}\right)$.

${s}_{12} = \frac{12}{2} \left(123 + 13\right)$

${s}_{12} = 6 \left(136\right)$

${s}_{12} = 816$

Hopefully this helps!