Find the 12th Term in Sequence 4n-2: Step-by-Step Solution

Q: What does n represent in the formula 4n - 2?

The variable n represents the position of the term you want to find. For the 1st term, n = 1. For the 12th term, n = 12. It's like asking 'which term do you want?' rather than 'what is the term's value?'

Q: Do I always follow the same steps for any sequence formula?

Yes! The process is always the same: identify the formula, substitute the position number for n, then calculate. Whether it's 4n - 2, 3n + 5, or any other formula, these steps work every time.

Q: How can I check if my answer of 46 is correct?

Substitute back into the original formula: $ 4(12) - 2 = 48 - 2 = 46 $. You can also check by finding a few other terms to see if the pattern makes sense!

Q: Why is this called an arithmetic sequence?

Actually, $ 4n - 2 $ generates an arithmetic sequence because each term increases by the same amount (4). The sequence goes: 2, 6, 10, 14... with a common difference of 4.

Arithmetic Sequences with Formula Substitution

The following is the rule to a sequence written in terms of $n$ :

$4n-2$

What is the 12th element of the sequence?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find member 12

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

00:09 Substitute appropriate values according to the data and solve to find the member

00:14 Always solve multiplication and division before addition and subtraction 00:27

00:25 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

The following is the rule to a sequence written in terms of $n$ :

$4n-2$

What is the 12th element of the sequence?

Step-by-step solution

To solve this problem, we'll follow these steps:

Identify the formula for the sequence: $a_n = 4n - 2$ .
Substitute $n = 12$ into the formula to find the 12th element.
Calculate the expression to determine the value of the 12th term.

Now, let's work through each step:

Step 1: Understand the sequence formula. The sequence is defined by $4n - 2$ , where $n$ is the term number.

Step 2: Substitute the value of $n = 12$ into the formula.
Calculating, we have:

$a_{12} = 4 \times 12 - 2$

Step 3: Perform the calculation.
$a_{12} = 48 - 2 = 46$

Therefore, the 12th element of the sequence is $46$ .

This matches choice 4, confirming our solution with the provided options.

Final Answer

$46$

Key Points to Remember

Essential concepts to master this topic

Sequence Rule: Use the given formula where n represents term position
Technique: Substitute n = 12 into 4n - 2 = 4(12) - 2
Check: Verify by calculating step-by-step: 48 - 2 = 46 ✓

Common Mistakes

Avoid these frequent errors

Using the term value instead of position number
Don't substitute the term's value for n instead of its position = completely wrong formula use! The variable n always represents which term you want (1st, 2nd, 12th), not the actual value of that term. Always use n as the position number in the sequence.

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

What does n represent in the formula 4n - 2?

The variable n represents the position of the term you want to find. For the 1st term, n = 1. For the 12th term, n = 12. It's like asking 'which term do you want?' rather than 'what is the term's value?'

Do I always follow the same steps for any sequence formula?

Yes! The process is always the same: identify the formula, substitute the position number for n, then calculate. Whether it's 4n - 2, 3n + 5, or any other formula, these steps work every time.

How can I check if my answer of 46 is correct?

Substitute back into the original formula: $4(12) - 2 = 48 - 2 = 46$ . You can also check by finding a few other terms to see if the pattern makes sense!

What if the formula was more complicated, like 2n² + 3?

The same method works! Just substitute carefully: for the 12th term, you'd calculate $2(12)² + 3 = 2(144) + 3 = 291$ . Always follow order of operations.

Why is this called an arithmetic sequence?

Actually, $4n - 2$ generates an arithmetic sequence because each term increases by the same amount (4). The sequence goes: 2, 6, 10, 14... with a common difference of 4.

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