Is 50 a Term in the Quadratic Sequence 2n²?

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.