find a formula for the nth term of the arithmetic sequence. first term -17 common difference 5 ( a_{n}=?n+ )

Explanation:

Step1: Recall the formula for the nth term of an arithmetic sequence

The formula for the nth term of an arithmetic sequence is (a_{n}=a_{1}+(n - 1)d), where (a_{1}) is the first term and (d) is the common difference.

Step2: Substitute the given values into the formula

Given (a_{1}=-17) and (d = 5), we have (a_{n}=-17+(n - 1)\times5).

Step3: Simplify the expression

[ \begin{align*} a_{n}&=-17+5n-5\ a_{n}&=5n-22 \end{align*} ]

Answer:

The first box (coefficient of (n)) is (5), and the second box is (-22). So (a_{n}=5n - 22)