# How do you find the sum of the terms of arithmetic -5, -3, -1,1......55?

Jun 12, 2016

We must first determine the number of terms. This can be done by using the formula ${t}_{n} = a + \left(n - 1\right) d$ and solving for $n$.

#### Explanation:

$55 = - 5 + \left(n - 1\right) 2$

$55 = - 5 + 2 n - 2$

$55 = - 7 + 2 n$

$62 = 2 n$

$31 = n$

Now, we can use the formula ${s}_{n} = \frac{n}{2} \left(2 a + \left(n - 1\right) d\right)$

${s}_{31} = \frac{31}{2} \left(2 \left(- 5\right) + \left(31 - 1\right) 2\right)$

${s}_{31} = \frac{31}{2} \left(50\right)$

${s}_{31} = 31 \times 25$

${s}_{31} = 775$

The sum of the terms is $775$.

Hopefully this helps!