Identify Terms in Sequence: Finding Values in an = 3n + 1

To solve this problem, we need to identify which of the given numbers is a term in the series defined by $a_n = 3n + 1$.

We will evaluate each choice:

• Substitute 36: $n = \frac{36 - 1}{3} = \frac{35}{3}$. This is not an integer, so 36 is not a term.
• Substitute 39: $n = \frac{39 - 1}{3} = \frac{38}{3}$. This is not an integer, so 39 is not a term.
• Substitute 33: $n = \frac{33 - 1}{3} = \frac{32}{3}$. This is not an integer, so 33 is not a term.
• Substitute 40: $n = \frac{40 - 1}{3} = \frac{39}{3} = 13$. This is an integer, so 40 is a term.

Therefore, the number 40 is a term in the series.

$40$