Calculate the 8th Term in the Sequence: Applying the Rule 2(2n-2)

Q: What does the formula 2(2n-2) actually represent?

This is the general term formula for the sequence. The variable n represents the position (1st, 2nd, 3rd, etc.), and when you substitute a specific position, you get the actual value at that position.

Q: Do I need to follow order of operations here?

Yes! Always work inside parentheses first: $ 2 \times 8 - 2 = 14 $, then multiply by the outside 2 to get $ 2 \times 14 = 28 $.

Q: What if I get a different formula format?

Sequence formulas can look different like $ a_n = 4n - 4 $, but the process is the same: substitute the position number for n and calculate. The key is careful arithmetic!

Q: Is there a pattern I can use instead of the formula?

While you could find patterns, using the given formula directly is more reliable and faster. Plus, it works for any term position, even very large ones like the 100th term!

Sequence Formulas with Direct Substitution

A sequence has a term-to-term rule of $2(2n-2)$ .

What is the 8th element of the sequence?

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Step-by-step video solution

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00:00 Find the 8th element in the sequence

00:03 The desired element's position according to the given data

00:07 We'll substitute the appropriate position in the formula and solve to find the element

00:11 Always solve parentheses first

00:14 Always solve multiplication and division before addition and subtraction

00:26 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A sequence has a term-to-term rule of $2(2n-2)$ .

What is the 8th element of the sequence?

Step-by-step solution

To find the 8th element of the sequence, we follow these steps:

Substitute $n = 8$ into the given sequence formula $a_n = 2(2n-2)$ .
Calculate $a_8 = 2 \times (2 \times 8 - 2)$ .
Simplify inside the parentheses: $2 \times 8 - 2 = 16 - 2 = 14$ .
Now compute $a_8 = 2 \times 14 = 28$ .

Therefore, the 8th element of the sequence is $28$ .

Final Answer

$28$

Key Points to Remember

Essential concepts to master this topic

Formula Application: Substitute the given position number directly into the sequence formula
Technique: Calculate $2(2 \times 8 - 2) = 2 \times 14 = 28$
Check: Verify by computing step-by-step: 16 - 2 = 14, then 2 × 14 = 28 ✓

Common Mistakes

Avoid these frequent errors

Confusing n with the term value
Don't substitute the term position as the answer = getting n = 8 instead of calculating! This skips the actual formula computation. Always substitute n into the complete formula and evaluate all operations.

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 does the formula 2(2n-2) actually represent?

This is the general term formula for the sequence. The variable n represents the position (1st, 2nd, 3rd, etc.), and when you substitute a specific position, you get the actual value at that position.

Do I need to follow order of operations here?

Yes! Always work inside parentheses first: $2 \times 8 - 2 = 14$ , then multiply by the outside 2 to get $2 \times 14 = 28$ .

How can I check if my answer is correct?

Substitute your result back or try calculating a simpler term first. For example, find the 1st term: $2(2 \times 1 - 2) = 2(0) = 0$ to verify your method works.

What if I get a different formula format?

Sequence formulas can look different like $a_n = 4n - 4$ , but the process is the same: substitute the position number for n and calculate. The key is careful arithmetic!

Is there a pattern I can use instead of the formula?

While you could find patterns, using the given formula directly is more reliable and faster. Plus, it works for any term position, even very large ones like the 100th term!

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