# How do you determine whether the sequence 10, 8, 6, 4, 2,... is arithmetic and if it is, what is the common difference?

Jul 28, 2017

common difference is$\text{ } - 2$

#### Explanation:

A sequence is arithmetic if the difference between consecutive terms is constant.

That is you add or subtract the same number to get the next term

In this case we have:

$10 , 8 , 6 , 4 , 2 , \ldots$

the differences between each terms are

$10 , \text{ "8," "6," "4," } 2 , \ldots$

$\text{ "darr" "darr" "darr" } \downarrow$

$\text{ "-2,-2,""-2," } - 2$

the differences are all the same so it is an Arithmetic sequence

the common difference is $- 2$