# How do you find the formula for a_n for the arithmetic sequence a_1=100, d=-8?

Jun 4, 2017

${a}_{n} = 108 - 8 n$

#### Explanation:

$\text{for the standard arithmetic sequence}$

$a , \textcolor{w h i t e}{x} a + d , \textcolor{w h i t e}{x} a + 2 d , \ldots . , a + \left(n - 1\right) d$

$\text{the nth term } = a + \left(n - 1\right) d$

$\text{here " a=a_1=100" and } d = - 8$

$\Rightarrow {a}_{n} = 100 - 8 \left(n - 1\right)$

$\textcolor{w h i t e}{\Rightarrow {a}_{n}} = 100 - 8 n + 8$

$\textcolor{w h i t e}{\Rightarrow {a}_{n}} = 108 - 8 n$