Calculate the Tenth Term in the Quadratic Sequence 2n²

Q: Do I multiply 2 × 10 first or square 10 first?

Always follow order of operations (PEMDAS/BODMAS)! Exponents come before multiplication, so calculate $ 10^2 = 100 $ first, then multiply by 2.

Q: What's the difference between 2n² and (2n)²?

Big difference! $ 2n^2 $ means multiply by 2 after squaring n, while $ (2n)^2 $ means multiply by 2 first, then square everything. For n=10: $ 2(10)^2 = 200 $ but $ (2 \times 10)^2 = 400 $!

Q: Why is this called a quadratic sequence?

Because the formula contains $ n^2 $ (n squared)! The highest power of n is 2, which makes it quadratic. These sequences grow much faster than linear sequences.

Q: Can I use a calculator for the squaring?

Absolutely! For larger values of n, calculators help avoid arithmetic errors. Just make sure you understand the process: substitute → square → multiply by coefficient.

Quadratic Sequences with Substitution Method

$2n^2$

What is the tenth term in the sequence above?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the tenth item in the sequence.

00:08 First, plug in the position, which is 10, into the formula. Let's go step by step.

00:21 Remember, always solve the exponents first. Keep up the great work!

00:30 And that's how we find our answer. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$2n^2$

What is the tenth term in the sequence above?

Step-by-step solution

To solve this problem, we'll determine the tenth term of the sequence based on the formula $2n^2$ .

Step 1: Recognize that the sequence is defined by $2n^2$ for any term $n$ .
Step 2: To find the tenth term, substitute $n = 10$ into the formula:

$2n^2 = 2(10)^2$

Step 3: Calculate the square of 10:

$(10)^2 = 100$

Step 4: Multiply by 2 to find the sequence value at that position:

$2 \times 100 = 200$

Therefore, the tenth term in the sequence is $200$ .

The correct answer choice is: $200$ .

Final Answer

200

Key Points to Remember

Essential concepts to master this topic

Formula Application: Substitute n = 10 directly into $2n^2$
Order of Operations: Calculate $10^2 = 100$ first, then multiply by 2
Verification: Check that $2(10)^2 = 2 \times 100 = 200$ ✓

Common Mistakes

Avoid these frequent errors

Calculating 2 × 10 = 20 before squaring
Don't calculate 2 × 10 first to get (20)² = 400! This ignores order of operations where exponents come before multiplication. Always calculate n² first, then multiply by the coefficient 2.

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

Do I multiply 2 × 10 first or square 10 first?

Always follow order of operations (PEMDAS/BODMAS)! Exponents come before multiplication, so calculate $10^2 = 100$ first, then multiply by 2.

What's the difference between 2n² and (2n)²?

Big difference! $2n^2$ means multiply by 2 after squaring n, while $(2n)^2$ means multiply by 2 first, then square everything. For n=10: $2(10)^2 = 200$ but $(2 \times 10)^2 = 400$ !

How do I find other terms in this sequence?

Just substitute different values of n! For the 5th term, use n=5: $2(5)^2 = 2 \times 25 = 50$ . For the 1st term, use n=1: $2(1)^2 = 2$ .

Why is this called a quadratic sequence?

Because the formula contains $n^2$ (n squared)! The highest power of n is 2, which makes it quadratic. These sequences grow much faster than linear sequences.

Can I use a calculator for the squaring?

Absolutely! For larger values of n, calculators help avoid arithmetic errors. Just make sure you understand the process: substitute → square → multiply by coefficient.

What if I get a decimal answer?

For this type of sequence with whole number inputs and integer coefficients, you should always get whole number answers. If you get a decimal, double-check your calculations!

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