# If S=(n(a+1))/2 what is n?

Mar 19, 2017

$n = \frac{2 S}{a + 1} \textcolor{w h i t e}{\text{XXX}}$provided $\left(a + 1\right) \ne 0$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX")S=(n(a+1))/2color(white)("XX}}$...at least that's how interpreted the question.

$\frac{n \left(a + 1\right)}{2} = S \textcolor{w h i t e}{\text{XXXX}}$because we usually like to have the variable we are solving for on the left.

$\rightarrow n \left(a + 1\right) = 2 S \textcolor{w h i t e}{\text{XXXX}}$after multiplying both sides by $2$

$\rightarrow n = \frac{2 S}{a + 1} \textcolor{w h i t e}{\text{XXXX}}$after multiplying both sides by $\left(a + 1\right)$ and with the assumption that $a \ne - 1$#