Is 8 a Term of the Quadratic Sequence 2n²?

Video Solution

Solution Steps

00:00 Is the number 8 a member of the sequence?

00:03 Let's substitute the term 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 term

00:11 Let's isolate N

00:23 When taking a root there are always 2 solutions, positive and negative

00:29 N must be positive, therefore this solution is not relevant

00:35 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll perform the following steps:

Step 1: Set up the equation $2n^2 = 8$ .
Step 2: Simplify the equation by dividing both sides by 2, resulting in $n^2 = 4$ .
Step 3: Solve for $n$ by taking the square root of both sides, leading to $n = \pm 2$ .
Step 4: Since sequence indices are positive integers, consider $n = 2$ .

Now, let's see if 8 is a term in the sequence:
Starting with the equation $2n^2 = 8$ :

$2n^2 = 8$

Step 2: Divide both sides by 2:

$n^2 = 4$

Step 3: Take the square root of both sides:

$n = \pm 2$

Since $n$ must be a positive integer for this sequence, we choose $n = 2$ .

This confirms that 8 can be expressed as $2(2^2) = 8$ . Thus, 8 is a term in the sequence.

Therefore, the solution to the problem is Yes.