# How do you write the nth term rule for the arithmetic sequence with d=4 and a_14=46?

Aug 13, 2016

${a}_{n} = 4 n - 10$

#### Explanation:

The nth term rule is ${a}_{n} = {a}_{1} + \left(n - 1\right) d$
To write the nth term rule we need to know both d and a.
We have $d = 4$ and the value of a_14#

${a}_{14} = a + \left(14 - 1\right) 4 = 46$

$a + 13 \times 4 = 46$

$a = - 6$

${a}_{n} = - 6 + \left(n - 1\right) 4$

${a}_{n} = - 6 + 4 n - 4$

${a}_{n} = 4 n - 10$