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.