# Find the term n=12, given the arithmetic sequence a_1=5 and d=1/3

Find the term n=12, given the arithmetic sequence ${a}_{1}=5$ and d=1/3
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wespee0
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:
$\text{XXX}{a}_{n}={a}_{1}+\left(n-1\right)\cdot d$
In this case with $n=12,{a}_{1}=5,\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}d=\frac{1}{3}$
$\text{XXX}{a}_{12}=5+\left(12-1\right)\cdot \frac{1}{3}=5+\frac{11}{3}=8\frac{2}{3}$