# What is the sum of the arithmetic sequence 3, 9, 15…, if there are 24 terms?

Mar 15, 2016

1728

#### Explanation:

We must first find the common difference, r.

$r = {t}_{2} - {t}_{1}$

$r = 9 - 3$

$r = 6$

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

n = 24

a = 3

r = 6

${s}_{24} = \frac{24}{2} \left(2 \left(3\right) + \left(24 - 1\right) 6\right)$

${s}_{24} = 12 \left(6 + 138\right)$

${s}_{24} = 12 \left(144\right)$

${s}_{24} = 1728$