# What is Sn for the arithmetic series with d = -4, an = 27, and n = 9?

Jan 30, 2016

$99$

#### Explanation:

We may use the formula for the sum to $n$ terms of an arithmetic series :

${\sum}_{k = 1}^{n} \left[a + \left(k - 1\right) d\right] = \frac{n}{2} \left[2 a + \left(n - 1\right) d\right]$

$= \frac{9}{2} \left[\left(2\right) \left(27\right) + \left(9 - 1\right) \left(- 4\right)\right]$

$= 99$