Is 8 a Term of the Quadratic Sequence 2n²?

$2n^2$

Is the number 8 a term in the sequence above?

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.