# What is the sum of the arithmetic sequence 8, 15, 22 …, if there are 26 terms?

Sep 27, 2016

$2483$

#### Explanation:

To calculate the $\textcolor{b l u e}{\text{sum of n terms}}$ for an arithmetic sequence.

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{S}_{n} = \frac{n}{2} \left[2 a + \left(n - 1\right) d\right]} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where a represents the first term and d, the common difference.

here a = 8, d = 22 - 15 = 15 - 8 = 7 and n = 26

$\Rightarrow {S}_{26} = \frac{26}{2} \left[\left(2 \times 8\right) + \left(25 \times 7\right)\right]$

$= 13 \left(16 + 175\right) = 2483$