# How do you find the next four terms of the arithmetic sequence -6, -2, 2,...?

May 6, 2018

$6 , 10 , 14 , 18$

#### Explanation:

Given: arithmetic sequence $- 6 , - 2 , 2 , \ldots$

${a}_{1} = - 6$

${a}_{2} = - 2$

${a}_{3} = 2$

The common difference $d = {a}_{2} - {a}_{1} = - 2 - \left(- 6\right) = 4$

To find the next four terms, just add $4$ to the next number.

Or, you can find ${a}_{n} = {a}_{1} + \left(n - 1\right) d$

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

${a}_{4} = - 6 + 4 \left(4 - 1\right) = - 6 + 12 = 6$

${a}_{5} = - 6 + 4 \left(5 - 1\right) = - 6 + 16 = 10$

${a}_{6} = - 6 + 4 \left(6 - 1\right) = - 6 + 20 = 14$

${a}_{7} = - 6 + 4 \left(7 - 1\right) = - 6 + 24 = 18$