# How do you determine whether each sequence is an arithmetic sequence: 18, 16, 15, 13,...?

The differences (or "gaps", if you will) between numbers in an arithmetic sequence are constant. This sequence is not an arithmetic sequence, because $18$ and $16$ differ by $2$, while $16$ and $15$ differ by only $1$. The terms do not have equal spacing, and so the series is not arithmetic.
The general way to test this for any sequence ${a}_{1} , {a}_{2} , {a}_{3} , \ldots$ is to check if $\left({a}_{2} - {a}_{1}\right) = \left({a}_{3} - {a}_{2}\right) = \left({a}_{4} - {a}_{3}\right) = \ldots = \left({a}_{n} - {a}_{n - 1}\right)$. If any of these equalities is invalid, the sequence is not arithmetic.