Question

write an equation for the sequence below. use $n$ to represent the position of a term in the sequence, where $n = 1$ for the first term.
7, 12, 17, 22, ...
write your answer using whole numbers, decimals, or simplified proper or improper fractions.
$a_n =$

Explanation:

Step1: Identify sequence type & common difference

The sequence is arithmetic. Calculate the common difference $d$:
$d = 12 - 7 = 5$

Step2: Recall arithmetic sequence formula

The general formula for the $n$-th term of an arithmetic sequence is:
$a_n = a_1 + (n-1)d$
where $a_1$ is the first term.

Step3: Substitute known values

Substitute $a_1=7$ and $d=5$ into the formula:
$a_n = 7 + (n-1) \times 5$

Step4: Simplify the expression

Expand and combine like terms:
$a_n = 7 + 5n - 5 = 5n + 2$

Answer:

$a_n = 5n + 2$