# How do you write the nth term rule for the arithmetic sequence with d=-6 and a_12=-4?

Nov 5, 2016

${t}_{n} = 68 - 6 n$.

#### Explanation:

The nth term rule is given by ${t}_{n} = a + \left(n - 1\right) d$, so we need to know the first term, $a$.

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

$- 4 = a + \left(12 - 1\right) - 6$

$- 4 = a - 66$

$62 = a$

We can now reinsert inside the formula:

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

${t}_{n} = 62 + \left(n - 1\right) - 6$

${t}_{n} = 62 - 6 n + 6$

${t}_{n} = 68 - 6 n$

Hopefully this helps!