# How do you find the term n=12, given the arithmetic sequence a_1=5 and d=1/3?

${a}_{12} = \textcolor{red}{8 \frac{2}{3}}$
The ${n}^{\text{th}}$ term, ${a}_{n}$ of an arithmetic sequence, with initial term, ${a}_{1}$ and incremental difference $d$ is given by the formula:
$\textcolor{w h i t e}{\text{XXX}} {a}_{n} = {a}_{1} + \left(n - 1\right) \cdot d$
In this case with $n = 12 , {a}_{1} = 5 , \text{ and } d = \frac{1}{3}$
$\textcolor{w h i t e}{\text{XXX}} {a}_{12} = 5 + \left(12 - 1\right) \cdot \frac{1}{3} = 5 + \frac{11}{3} = 8 \frac{2}{3}$