# How do you find the formula for a_n for the arithmetic sequence a_1=-y, d=5y?

Aug 26, 2017

${u}_{n} = \left(5 n - 6\right) y$

#### Explanation:

If we have $n$ terms of an AP, with first term $a$, and common difference $d$ the terms are:

$\left\{a , a + d , a + 2 d , \ldots , a + \left(n - 1\right) d\right\}$

Assuming ${a}_{1}$ is the first term (as opposed to ${a}_{0}$) then we have:

$a = - y$
$d = 5 y$

So the ${n}^{t h}$ term us:

${u}_{n} = - y + \left(n - 1\right) 5 y$
$\setminus \setminus \setminus \setminus = \left(5 n - 6\right) y$