Find If 5 Is in the Arithmetic Sequence: Solve 2n - 1

Question

$2n-1$

Is the number 5 a term in the above sequence?

00:06 Is the number 5 part of the sequence?

00:10 We'll plug 5 into the sequence formula, and solve for N.

00:15 If N is a positive whole number, it tells us the position of 5.

00:21 Let's focus on solving for N now.

00:36 Great! That's how we find our answer.

To determine if the number 5 is a term in the sequence given by $a_n = 2n - 1$ , we need to find a positive integer $n$ such that $2n - 1 = 5$ .

Let's solve the equation:

1. Start with the equation: $2n - 1 = 5$

2. Add 1 to both sides to isolate the term involving $n$ : $2n = 6$

3. Divide both sides by 2 to solve for $n$ : $n = 3$

Since $n = 3$ is a positive integer, the number 5 is indeed a term in the sequence. Therefore, the correct answer is Yes.

Yes