# How do you find a_21 given 121, 118, 115, ...?

Dec 11, 2016

If $a \left(1\right) = 121$, $a \left(2\right) = 118$, and $a \left(3\right) = 115$, we can create an equation for $a \left(n\right)$, then plug in $n = 21$ to get $a \left(21\right)$.

$a \left(n\right) = - 3 n + b$
$121 = - 3 \left(1\right) + b$
$b = 124$

$a \left(n\right) = - 3 n + 124$

$a \left(21\right) = - 3 \left(21\right) + 124$
$= 61$