{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
{{ searchError }}
search
{{ courseTrack.displayTitle }}
{{ printedBook.courseTrack.name }} {{ printedBook.name }}

# Writing and Using Explicit Rules for Arithmetic Sequences

## Writing and Using Explicit Rules for Arithmetic Sequences 1.3 - Solution

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 $n.$
$a_n=5+(n-1)(\text{-}3)$
$a_{{\color{#0000FF}{2}}}=5+({\color{#0000FF}{2}}-1)(\text{-}3)$
$a_{2}=5+(1) (\text{-}3)$
$a_{2}=5+(\text{-}3)$
$a_{2}=5-3$
$a_{2}=2$
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 $\text{-} 25.$