# Is the following an arithmetic sequence? 5, 0, -5, -10,.?

Aug 9, 2016

yes

#### Explanation:

An arithmetic sequence is a sequence that has a pattern of addition or subtraction of the same number. Note that the first 4 terms of $5 , 0 , - 5 , - 10 , \ldots$ can be derived from

${\sum}_{i}^{n} - 5 \left(i\right) + 5$

One rule of thumb to try is to subtract sequential terms and see if they are the same. Doing so will yield $- 5$.