# How do you write a rule for the nth term of the arithmetic sequence given d=-3, a_2=18?

Nov 26, 2017

${a}_{n} = 24 - 3 n$

#### Explanation:

$\text{the nth term of an arithmetic sequence is}$

•color(white)(x)a_n=a+(n-1)d

$\text{where a is the first term and d the common difference}$

$\text{we have to find a}$

${a}_{2} = a + d = 18$

$\Rightarrow a - 3 = 18 \Rightarrow a = 21$

$\Rightarrow {a}_{n} = 21 - 3 \left(n - 1\right)$

$\textcolor{w h i t e}{\Rightarrow {a}_{n}} = 21 - 3 n + 3$

$\Rightarrow {a}_{n} = 24 - 3 n$