# How do you write the nth term rule for the arithmetic sequence with d=-12 and a_1=80?

Jul 30, 2016

${n}^{t h}$ term is $92 - 12 n$

#### Explanation:

If in a arithmetic sequence, ${a}_{1}$ is first term and common difference is $d$, the ${n}^{t h}$ term is given by ${a}_{n} = a + \left(n - 1\right) d$

As ${a}_{1} = 80$ and $d = - 12$, ${n}^{t h}$ term is

${a}_{n} = 80 + \left(n - 1\right) \times \left(- 12\right)$

= $80 - 12 n + 12$

= $92 - 12 n$