# The terms of a sequence are -2, -6, -10, -14, -18, what is the common difference, explicit and recursive formula?

Feb 19, 2017

The common difference is $- 4$;

The explicit formula is ${a}_{n} = - 2 - 4 \left(n - 1\right) , n > 0 , n \in \mathbb{N}$

The recursive formula is ${a}_{1} = - 2 \mathmr{and} {a}_{n + 1} = {a}_{n} - 4$

#### Explanation:

This is an arithmetic sequence. since you can find a common difference, that is

$- 6 - \left(- 2\right) = - 10 - \left(- 6\right) = - 14 - \left(- 10\right) = - 18 - \left(- 14\right) = - 4$

The explicit formula is:

${a}_{n} = - 2 - 4 \left(n - 1\right) , n > 0 , n \in \mathbb{N}$

The recursive formula is:

${a}_{1} = - 2 \mathmr{and} {a}_{n + 1} = {a}_{n} - 4$