Find the 8th Term in the Arithmetic Sequence: 2, 5, 8, ...

Question

Assuming the sequence continues according to the same rule, what number appears in the 8th element?

$2,5,8\ldots$

00:00 Find the 8th term

00:03 This is the sequence formula

00:06 Let's substitute the appropriate term position in the formula and solve

00:12 Always solve multiplication and division before addition and subtraction

00:18 And this is the solution to the question

To solve for the 8th element in the sequence, follow these steps:

Step 1: Identify the sequence pattern.
Calculate the differences: $5 - 2 = 3$ and $8 - 5 = 3$ . This pattern shows the sequence increases by 3 each time, indicating an arithmetic sequence with common difference $d = 3$ .
Step 2: Use the arithmetic sequence formula $a_n = a_1 + (n-1) \cdot d$ .
Given $a_1 = 2$ , $d = 3$ , and $n = 8$ :
Substitute these values into the formula:
$a_8 = 2 + (8-1) \cdot 3$
$a_8 = 2 + 7 \cdot 3$
$a_8 = 2 + 21$
$a_8 = 23$

Therefore, the 8th element in the sequence is $23$ .