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?

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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

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

FAQ

Everything you need to know about this question

What if I get a negative value for n?

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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?

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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?

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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?

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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?

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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.

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Determine whether the number is an element in the sequence