Answer
$a_n = 3n - 2$
Work Step by Step
First, find the pattern of the sequence in terms of how it relates to $n$, the order of the term in the sequence.
$a_1 = 3(1) - 2 = 3 - 2 = 1$
$a_2 = 3(2) - 2 = 6 - 2 = 4$
$a_3 = 3(3) - 2 = 9 - 2 = 7$
$a_4 = 3(4) - 2 = 12 - 2 = 10$
It looks like two is subtracted from three times each term; therefore, the explicit formula is:
$a_n = 3n - 2$
