How do you find the next three terms of the arithmetic sequence -2, -5, -8, -11,...?

Apr 22, 2017

$- 14 , - 17 , - 20$

Explanation:

$\text{the terms of an arithmetic sequence are}$

$a , a + d , a + 2 d , a + 3 d , \ldots \ldots . . , a + \left(n - 1\right) d$

$\text{where d is the common difference between each term}$

$d = {a}_{2} - {a}_{1} = {a}_{3} - {a}_{2} = \ldots . = {a}_{n} - {a}_{n - 1}$

$\text{here } d = - 5 - \left(- 2\right) = - 3$

$\text{to obtain the next term in the sequence,}$
$\text{subtract 3 from the previous term}$

$\Rightarrow - 11 - 3 = - 14$

$- 14 - 3 = - 17 \text{ and } - 17 - 3 = - 20$