# How do you find the explicit formula for the following sequence 57, 66, 75, 84, 93, ...?

Apr 14, 2016

${n}_{t h}$ of the series is given by $9 n + 48$

#### Explanation:

As the difference between a term and its preceding term is always $9$, it is an arithmetic sequence of type

$\left\{a , a + d , a + 2 d , a + 3 d , a + 4 d , a + 5 d , \ldots \ldots \ldots .\right\}$

If $a$ is the first term of such a series and $d$ is the difference between a term and its preceding term,

${n}_{t h}$ of the series is given by $a + \left(n - 1\right) d$.

Here $a = 57$ and $d = 9$, hence

${n}_{t h}$ of the series is given by $57 + 9 \left(n - 1\right) = 9 n + 48$.