Answer
$a_n = 5 + (n - 1)(-3)$
Work Step by Step
Let's look at the terms to see if we can find a pattern:
$a_1 = 5$
$a_2 = 5 -3 = 2$
$a_3 = 2 - 3 = -1$
$a_4 = -1 - 3 = -4$
It looks like to get the next term, $-3$ is added to the previous term; therefore, this is an arithmetic sequence because we are adding the same number to the previous term to get the next term.
Use the explicit formula for arithmetic sequences, which is $a_n = a + (n - 1)d$, where $a$ is the first term of the sequence and $d$ is the common difference; in this exercise, $a$ is $5$ and $d$ is $-3$:
$a_n = 5 + (n - 1)(-3)$
