# How do you write a rule for the nth term of the arithmetic sequence given d=1/2, a_5=20?

Jul 12, 2018

${a}_{n} = \frac{1}{2} n + \frac{35}{2}$

#### Explanation:

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

•color(white)(x)a_n=a_1+(n-1)d

$\text{we require to find } {a}_{1}$

${a}_{5} = {a}_{1} + \left(4 \times \frac{1}{2}\right) = 20 \Rightarrow {a}_{1} = 18$

${a}_{n} = 18 + \frac{1}{2} \left(n - 1\right)$

$\textcolor{w h i t e}{{a}_{n}} = 18 + \frac{1}{2} n - \frac{1}{2}$

$\textcolor{w h i t e}{{a}_{n}} = \frac{1}{2} n + \frac{35}{2} \leftarrow \textcolor{red}{\text{ n th term formula}}$