# How do you find the term n=20, given the arithmetic sequence a_1=-4 and d=-9?

Jun 13, 2018

${a}_{20} = - 175$. See below

#### Explanation:

An arithmetic sequence has the general term given by

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

Then applying given values

${a}_{n} = - 4 + \left(n - 1\right) \left(- 9\right) = - 4 - 9 n + 9 = - 9 n + 5$

For $n = 20$, we have a_20=-9·20+5=-175