# How do you find the explicit formula for the following sequence 38, 33, 28, 23,...?

Mar 15, 2016

$\left({x}_{n}\right) = 43 - 5 n$

#### Explanation:

This is an arithmetic sequence with first term $a = 38$ and constant difference $d = 5$.

Hence the general term is given by
$\left({x}_{n}\right) = a + \left(n - 1\right) d$
$= 38 + \left(n - 1\right) \left(- 5\right)$
$= 38 - 5 n + 5$
$= 43 - 5 n$