# What is the sum of the first 18 terms of the arithmetic series 11+15+19+23+...?

Aug 21, 2017

$810$

#### Explanation:

The required formula is $\textcolor{red}{{S}_{n} = \frac{n}{2} \left[2 a + \left(n - 1\right) d\right]}$

Where,

${S}_{n}$ is the sum of $n$ terms
$n$= the number of terms, $\text{ } n = 18$
$a$ = the first term, $\textcolor{w h i t e}{\times \times \times x} a = 11$
$d =$ the common difference, $\text{ } d = 4$

Substituting these values gives:

${S}_{18} = \frac{18}{2} \left[2 \left(11\right) + \left(18 - 1\right) \left(4\right)\right]$

$= 9 \left[22 + 17 \times 4\right]$

$= 9 \left[22 + 68\right]$

$= 9 \left[90\right]$

$= 810$