Answer:
Step-by-step explanation:
Since the sequence is increasing by a constant factor ([tex]3[/tex]) each time, we know that this is an arithmetic sequence.
The formula for an arithmetic sequence is the following:
[tex]a_{n} = a_{1} + (n - 1)d[/tex]
Where [tex]n[/tex] is the number in the sequence and [tex]d[/tex] is the constant that the sequence is increasing by.
Based on all of the information given, we know that [tex]a_{1} = 2[/tex] (since [tex]2[/tex] is the first number in the sequence), and [tex]d = 3[/tex], so we can construct the formula:
[tex]a_{n} = 2 + (n - 1)3[/tex]
[tex]a_{n} = 2 + 3n - 3[/tex]
[tex]a_{n} = 3n - 1[/tex]
