Arithmetic Sequence: Finding Difference Between 24th and 21st Terms

What is the difference between the value of the 24th element and the value of the 21st element of the sequence below?

$2,5,8\ldots$

Given the sequence $2, 5, 8, \ldots$, we will find the difference between the 24th and 21st terms.

First, identify the parameters of the sequence:
The first term $a_1 = 2$.
The common difference $d$ is $5 - 2 = 3$.

The formula for the nth term of an arithmetic sequence is given by:

$a_n = a_1 + (n-1)d$

Let's find the 24th term:

$a_{24} = a_1 + (24-1) \cdot d = 2 + 23 \cdot 3$

$a_{24} = 2 + 69 = 71$

Next, find the 21st term:

$a_{21} = a_1 + (21-1) \cdot d = 2 + 20 \cdot 3$

$a_{21} = 2 + 60 = 62$

Now calculate the difference between these terms:

$a_{24} - a_{21} = 71 - 62 = 9$

Therefore, the difference between the 24th and 21st terms of the sequence is 9.