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?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find member number 12.

00:12 First, locate where member 12 is in the data.

00:17 Next, substitute the right values and solve for member 12.

00:22 Remember, always do multiplication and division, before addition and subtraction.

00:33 And that's how you find the solution. Great job!

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

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

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.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Series questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime