3n+1 Sequence: Identifying Valid Elements

To determine which number is an element of the sequence $3n + 1$, we will check all the given choices to see if they can be represented in this form with an integer $n$.

• Consider Choice 1: $x = 15$

Calculation: $n = \frac{15 - 1}{3} = \frac{14}{3} = 4.67$

This is not an integer, so 15 is not part of the sequence.

• Consider Choice 2: $x = 17$

Calculation: $n = \frac{17 - 1}{3} = \frac{16}{3} = 5.33$

This is not an integer, so 17 is not part of the sequence.

• Consider Choice 3: $x = 16$

Calculation: $n = \frac{16 - 1}{3} = \frac{15}{3} = 5$

This is an integer, so 16 is part of the sequence.

• Consider Choice 4: $x = 18$

Calculation: $n = \frac{18 - 1}{3} = \frac{17}{3} = 5.67$

This is not an integer, so 18 is not part of the sequence.

Therefore, the correct choice is $\textbf{16}$, as it is the number that fits the sequence $3n + 1$ for an integer $n$.