Writing and Using Explicit Rules for Arithmetic Sequences

To find certain terms in a sequence described by an explicit formula, substitute the number of the desired term into the formula to get the term's value. For the given explicit formula, $\begin{gathered} a_n=5+(n-1)(\text{-}3), \end{gathered}$ we can find the ${\color{#0000FF}{\text{second}}},$ ${\color{#009600}{\text{fourth}}},$ and ${\color{#FF0000}{\text{eleventh}}}$ terms of the sequence by substituting ${\color{#0000FF}{2}},$ ${\color{#009600}{4}},$ and ${\color{#FF0000}{11}}$ into the formula for $n.$ Now, let's do the same thing for the ${\color{#009600}{\text{fourth}}}$ and ${\color{#FF0000}{\text{eleventh}}}$ terms.

$n^{\text{th}}$ term	$5+(n-1)(\text{-} 3)$	$a_n$
${\color{#0000FF}{2}}$	$5+({\color{#0000FF}{2}}-1)(\text{-} 3)$	$2$
${\color{#009600}{4}}$	$5+({\color{#009600}{4}}-1)(\text{-} 3)$	$\text{-} 4$
${\color{#FF0000}{11}}$	$5+({\color{#FF0000}{11}}-1)(\text{-} 3)$	$\text{-} 25$

The second, fourth, and eleventh terms are $2,$ $\text{-} 4,$ and $\text{-} 25.$