Question

Write an expression for the apparent nth term(a) of the sequence. 2,5,8,11,14...

Answer 1

Answer:

Step-by-step explanation:

Since the sequence is increasing by a constant factor ($3$) each time, we know that this is an arithmetic sequence.

The formula for an arithmetic sequence is the following:

$a_{n} = a_{1} + (n - 1)d$

Where $n$ is the number in the sequence and $d$ is the constant that the sequence is increasing by.

Based on all of the information given, we know that $a_{1} = 2$ (since $2$ is the first number in the sequence), and $d = 3$, so we can construct the formula:

$a_{n} = 2 + (n - 1)3$

$a_{n} = 2 + 3n - 3$

$a_{n} = 3n - 1$