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

Question

Given the series, y represents some term in the series and n represents the position of the term in the series.

Only one of the following is a term in the series, reveal it:

$a_n=3n+1$

00:00 Find which of the following is a member of the sequence

00:04 We'll substitute this solution in the formula and solve for X

00:09 If the solution for X is positive and whole, then it's a member of the sequence

00:12 Let's isolate X

00:19 And this is the solution to the question

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.

$40$

$40$