# How do you find the formula for a_n for the arithmetic sequence 10, 5, 0, -5, -10, ...?

Feb 27, 2017

${a}_{n} = 15 - 5 n$

#### Explanation:

We know the first term and the common difference.

${t}_{n} = a + \left(n - 1\right) d$

${t}_{n} = 10 + \left(n - 1\right) - 5$

${t}_{n} = 10 - 5 n + 5$

${t}_{n} = 15 - 5 n$

Note that ${a}_{n}$ and ${t}_{n}$ are equivalent terms.

Hopefully this helps!