# How do you find the next three terms of the arithmetic sequence 22, 20, 18, 16,...?

Apr 5, 2018

$\textcolor{b l u e}{12 , 10 , 8}$

#### Explanation:

The $n t h$ term of an arithmetic sequence is given by:

$a + \left(n - 1\right) d$

Where:

$\boldsymbol{a}$ is the first term.

$\boldsymbol{d}$ is the common difference.

$\boldsymbol{n}$ is the $n t h$ term.

If $a , b , c$ are in arithmetic sequence, then:

$b - a = c - b$

This is called the common difference:

We have:

$22 , 20 , 18 , 16 , \ldots$

$\therefore$

$20 - 22 = 18 - 20 = - 2$

$d = - 2$

First term is $20$

$a = 20$

We need 5th , 6th and 7th terms:

Using:

$a + \left(n - 1\right) d$

$5 t h = 20 + \left(5 - 1\right) \left(- 2\right) = 12$

$6 t h = 20 + \left(6 - 1\right) \left(- 2\right) = 10$

$7 t h = 20 + \left(7 - 1\right) \left(- 2\right) = 8$

$\therefore$

$22 , 20 , 18 , 16 , \textcolor{b l u e}{12 , 10 , 8 ,} \ldots$