Is 50 a Term in the Quadratic Sequence 2n²?

Quadratic Sequences with Integer Solutions

$2n^2$

Is the number 50 a term in the sequence above?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's find out if the number thirty is in our sequence.

00:08 To do this, we'll plug thirty into the sequence formula and solve for N.

00:13 If N is a positive whole number, then thirty is indeed a term in the sequence.

00:19 Okay, let's focus on isolating N in our equation.

00:29 Remember, when we take a square root, we get two solutions: one positive and one negative.

00:35 We need N to be positive, so we can ignore the negative solution.

00:41 And that's how we solve the problem! Great job, everyone!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$2n^2$

Is the number 50 a term in the sequence above?

2

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.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: Set sequence formula equal to given term value
Technique: Solve $2n^2 = 50$ by dividing: $n^2 = 25$
Check: Verify $n = 5$ is positive integer: $2(5)^2 = 50$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to check if n is a positive integer
Don't just solve $n^2 = 25$ and stop at n = ±5! Negative values don't make sense for sequence positions. Always verify that n is a positive whole number for valid sequence terms.

Practice Quiz

Test your knowledge with interactive questions

Look at the following set of numbers and determine if there is any property, if so, what is it?

$\( 94,96,98,100,102,104 \)$

FAQ

Everything you need to know about this question

What if I get a negative value for n?

+

If you get a negative value, the number is not a term in the sequence. Sequence positions (n values) must be positive integers like 1, 2, 3, 4, etc.

What if n comes out as a decimal or fraction?

+

If n is not a whole number, then the given number is not a term in the sequence. For example, if $n = 3.5$ , there's no 3.5th position in a sequence!

Why do we only consider the positive square root?

+

In sequences, the position number (n) represents which term you're looking at. You can't have the -5th term in a sequence - positions start at 1, 2, 3, and so on.

How do I double-check my work?

+

Substitute your n value back into the original formula. If $n = 5$ , then $2(5)^2 = 2(25) = 50$ . The result should match the number you were asked about!

What if the equation has no real solutions?

+

If you get something like $n^2 = -25$ , there's no real solution since you can't take the square root of a negative number. This means the number is not a term in the sequence.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Series questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations

Series / Sequences

Verify if 30 is a Term in the Sequence an = 15n: Term Investigation

Finding Zero in the Sequence: Solve for n in 3n - 3

Solve the Sequence Equation: Is 1 a Term in 15n - 20?

Is 30 a Term in the Sequence Defined by 6n?

Topic Navigation

Main Subject:

Series

209 questions • 1 categories

Articles in this Subject:

Recurrence Relations

Specific Subject:

Series / Sequences

207 questions • 1 question types

Articles in this Subject:

Recurrence Relations Sequences

Question Types in this Subject:

Determine whether the number is an element in the sequence