College Algebra, Chapter 9, 9.2, Section 9.2, Problem 42

Suppose the first term of an arithmetic sequence is $1$ and the common difference is $4$. Is $11,937$ a term of this sequence? If so, which term is it?

Here we have $a = 1$ and $d = 4$, so the nth term is

$a_n = 1 + 4(n-1)$

Solve for $n$, if $a_n = 11,937$. So,


$
\begin{equation}
\begin{aligned}

11,937 =& 1 + 4(n-1)
&& \text{Substitute } a_n = 11,937
\\
\\
11,937 =& 1+4n-4
&& \text{Distributive Property}
\\
\\
11,937 =& 4n-3
&& \text{Simplify}
\\
\\
4n =& 11,937 +3
&& \text{Add } 3
\\
\\
n =& \frac{11,940}{4}
&& \text{Divide by } 4
\\
\\
n =& 2,985
&&

\end{aligned}
\end{equation}
$


$11,937$ is the $2,985$th term of this sequence.