# How do you determine whether each sequence is an arithmetic sequence: 4, 9, 14, 19...?

##### 1 Answer
Oct 24, 2017

$\text{arithmetic sequence}$

#### Explanation:

$\text{the standard arithmetic sequence is}$

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

$\text{where a is the first term and d is the "color(blue)"common difference}$

•color(white)(x)d=a_2-a_1=a_3-a_2=a_n-a_(n-1)

$\text{here } d = 9 - 4 = 14 - 9 = 19 - 14 = 5$

$\text{there is a common difference of 5 between the terms}$

$\Rightarrow \text{the given terms form an arithmetic sequence}$