# Find the formula for a_n for the arithmetic sequence a_1=5,a_4=15

Find the formula for ${a}_{n}$ for the arithmetic sequence ${a}_{1}=5,{a}_{4}=15$
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indyterpep
the nth term of an arithmetic sequence is
$•x{a}_{n}={a}_{1}+\left(n-1\right)d$
where d is the common difference
$\text{given}\phantom{\rule{1ex}{0ex}}{a}_{4}=15\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}{a}_{1}=5$
$⇒5+3d=15⇒d=\frac{10}{3}$
$⇒{a}_{n}=5+\frac{10}{3}\left(n-1\right)$
$⇒{a}_{n}=5+\frac{10}{3}n-\frac{10}{3}$
$⇒{a}_{n}=\frac{10}{3}n+\frac{5}{3}$