Is 50 a Term in the Quadratic Sequence 2n²?

Video Solution

Solution Steps

00:00 Is the number 30 a member of the sequence?

00:03 Let's substitute the member into 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

00:24 When taking a root there are always 2 solutions, positive and negative

00:30 N must be positive, therefore this solution is not relevant

00:36 And this is the solution to the question

Step-by-Step Solution

To determine if 50 is a term in the sequence defined by $2n^2$ , we will solve the equation $2n^2 = 50$ for $n$ .

Step 1: Simplify the equation.
Divide both sides of the equation by 2:
$\frac{2n^2}{2} = \frac{50}{2}$
This simplifies to:
$n^2 = 25$

Step 2: Solve for $n$ .
Take the square root of both sides:
$\sqrt{n^2} = \sqrt{25}$
Thus, $n = 5$ .

Step 3: Check if $n$ is a positive integer.
Since $n = 5$ is indeed a positive integer, 50 is a term in the sequence.

Therefore, the number 50 is a term in the sequence $2n^2$ , and the answer is Yes.