# What is the sum of the arithmetic series 6 + 12 + 18 + ... + 60?

Jan 22, 2016

The common difference $d = 12 - 6 = 6$

Now, determine what term is 60?

#### Explanation:

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

$60 = 6 + \left(n - 1\right) \left(6\right)$

$n = 10$

Now that we know 60 is the 10th term , use the sum formula ...

sum $= \frac{{a}_{1} + {a}_{n}}{2} \times n$

sum $= \frac{6 + 60}{2} \times 10 = 330$

hope that helped