# How do you find the explicit formula for the following arithmetic sequence 123, 116, 109, 102, 95, ...?

Apr 22, 2018

${a}_{n} = 123 - 7 \left(n - 1\right)$

#### Explanation:

When defined explicitly:
${a}_{n} = {a}_{1} + d \left(n - 1\right)$

${a}_{n}$ is the nth term
${a}_{1}$ is the first term
$d$ is the difference

The difference is:
$116 - 123 = - 7$

So this can be written as:
${a}_{n} = 123 - 7 \left(n - 1\right)$