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

Question

$2n-1$

Is the number 5 a term in the above sequence?

00:00 Is the number 5 a member of the sequence?

00:04 Let's substitute the member in the sequence formula and solve for N

00:08 If the solution for N is positive and whole, then this is the position of the member

00:14 Let's isolate N

00:30 And this is the solution to the question

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