Find the 7th Term in Sequence: 2(2n-2) Step-by-Step

Q: Do I always need to simplify the formula before substituting?

While not strictly required, simplifying first makes calculations easier and reduces errors. Compare $ 2(2n-2) $ versus $ 4n-4 $ - the simplified version is much cleaner!

Q: What does n represent in sequence formulas?

n represents the position number of the term you want to find. For the 7th term, n = 7. For the 1st term, n = 1. It's like the "address" of each term in the sequence.

Q: How do I know if I substituted correctly?

Double-check by asking: "Did I replace every n with 7?" In $ 4n-4 $, there's only one n, so it becomes $ 4(7)-4 $.

Sequence Terms with Substitution Method

Below is the rule for a sequence in terms of $n$ :

$2(2n-2)$

What is the value of the 7th element in the sequence?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the 7th element

00:04 Location of the desired element according to the data

00:11 Substitute appropriate values according to the data and solve to find the element

00:23 Always solve parentheses first

00:27 Always solve multiplication and division before addition and subtraction

00:38 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

Below is the rule for a sequence in terms of $n$ :

$2(2n-2)$

What is the value of the 7th element in the sequence?

Step-by-step solution

To determine the 7th element of the sequence defined by the rule $2(2n - 2)$ , we follow these steps:

Step 1: Identify the given formula for the sequence, which is $2(2n - 2)$ .
Step 2: Simplify this formula to its basic form. By expanding, we have: $2 \times (2n - 2) = 4n - 4.$
Step 3: Substitute $n = 7$ into the simplified formula $4n - 4$ .
Step 4: Perform the calculation:
$\begin{aligned} 4n - 4 &= 4 \times 7 - 4 \\ &= 28 - 4 \\ &= 24 \end{aligned}$

Thus, the 7th element of the sequence is $\boldsymbol{24}$ .

Final Answer

$24$

Key Points to Remember

Essential concepts to master this topic

Formula: Use given rule $2(2n-2)$ and substitute position value
Technique: Simplify first: $2(2n-2) = 4n-4$ , then substitute $n=7$
Check: Verify calculation: $4(7)-4 = 28-4 = 24$ ✓

Common Mistakes

Avoid these frequent errors

Substituting n = 7 into the original formula without simplifying
Don't calculate 2(2×7-2) = 2(14-2) = 2(12) = 24 directly without simplifying! While this gives the correct answer, it's harder and more error-prone with complex formulas. Always simplify the formula first to 4n-4, then substitute n = 7.

Practice Quiz

Test your knowledge with interactive questions

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

FAQ

Everything you need to know about this question

Do I always need to simplify the formula before substituting?

While not strictly required, simplifying first makes calculations easier and reduces errors. Compare $2(2n-2)$ versus $4n-4$ - the simplified version is much cleaner!

What does n represent in sequence formulas?

n represents the position number of the term you want to find. For the 7th term, n = 7. For the 1st term, n = 1. It's like the "address" of each term in the sequence.

How do I know if I substituted correctly?

Double-check by asking: "Did I replace every n with 7?" In $4n-4$ , there's only one n, so it becomes $4(7)-4$ .

What if I get a negative answer?

Negative sequence terms are perfectly valid! Just follow the same steps: substitute the position number and calculate carefully, keeping track of positive and negative signs.

Can I check my answer another way?

Yes! Calculate a few nearby terms like the 6th and 8th terms. If your sequence is $4n-4$ , the 6th term is 20 and 8th term is 28, so 24 for the 7th term makes sense!

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