# How do you find a1 in the arithmetic series with s7=287 and d=12?

Apr 6, 2016

${a}_{1} = 215$

#### Explanation:

For an arithmetic series with initial term ${a}_{1}$ and difference between terms of $d$
$\textcolor{w h i t e}{\text{XXX}} {a}_{n} = {a}_{1} + \left(n - 1\right) d$

We are told $d = 12$
and${a}_{7} = 287$

So
$\textcolor{w h i t e}{\text{XXX}} {a}_{7} = \textcolor{b l u e}{287} = {a}_{1} + \left(7 - 1\right) \times 12 = \textcolor{b l u e}{{a}_{1} + 72}$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow {a}_{1} = 287 - 72 = 215$