Exercise 55 Page 206

We can define an arithmetic sequence as a function of $n.$ This function generates the terms of any arithmetic sequence given a certain starting value $a_1$ and common difference $d.$ The variable $n$ is the independent variable and will always be a counting number. It represents the position of the term within the sequence. Therefore, the arithmetic sequence will have the following terms. From the given diagram we can identify a few elements in our arithmetic sequence. We already know that the first term $a_1$ is $23.$ Now, to find the value of $d,$ we will substitute the information for $4\text{th}$ term in the above equation. In other words, we will substitute $4$ for $n$ and $41$ for $f(n).$ The common difference is $6.$ Let's use this information to write the function. Finally, let's distribute $6$ in the above equation, and simplify the right-hand side.