# What is the recursive formula for the sequence 4, 12, 20,... ?

Feb 22, 2017

$\left\{\begin{matrix}{a}_{1} = 4 \\ {a}_{n + 1} = {a}_{n} + 8 \text{ for } n \ge 1\end{matrix}\right.$

#### Explanation:

As far as it goes, this is an arithmetic sequence with common difference $8$, since:

$12 - 4 = 8$

$20 - 12 = 8$

So we can describe it recursively by:

$\left\{\begin{matrix}{a}_{1} = 4 \\ {a}_{n + 1} = {a}_{n} + 8 \text{ for } n \ge 1\end{matrix}\right.$

Alternatively, a direct formula is given by:

${a}_{n} = 4 + 8 \left(n - 1\right)$

or if you prefer:

${a}_{n} = 8 n - 4$