# How do you write an explicit formula for the general term of the sequence [-4,2,8,14,...]?

Jul 17, 2015

The explicit formula for the sequence is $\textcolor{red}{{a}_{n} = 6 n - 10}$.

#### Explanation:

This looks like an arithmetic sequence, so we start by finding the common difference $d$.

d = a_n – a_(n-1)

Your sequence is [-4,2,8,14,…].

For ${a}_{2}$, d = a_2 - a_1 = 2–(-4) = 2+4 = 6

For ${a}_{3}$, $d = {a}_{3} - {a}_{2} = 8 - 2 = 6$

For ${a}_{4}$, $d = {a}_{4} - {a}_{3} = 14 - 8 = 6$

So $d = 6$.

The general formula for an arithmetic sequence is

${a}_{n} = {a}_{1} + \left(n - 1\right) d$.

So, for your sequence, the general formula is

${a}_{n} = - 4 + 6 \left(n - 1\right) = - 4 + 6 n - 6$.

${a}_{n} = 6 n - 10$