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

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

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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