Find the Position of 18 in the Sequence 4n-2: Term Identification

Q: What if I get a decimal or fraction for n?

If $ n $ is not a positive integer, then the number is not part of the sequence! Term positions must be whole numbers like 1, 2, 3, etc.

Q: How do I know if 18 is actually in the sequence?

Solve the equation $ 4n - 2 = 18 $. If you get a positive integer for $ n $, then 18 is the nth term of the sequence.

Q: Can I just substitute different values of n until I find 18?

You could, but it's much faster to solve algebraically! Plus, if the number isn't in the sequence, you'd waste time guessing forever.

Q: What does the formula 4n-2 actually mean?

It's an arithmetic sequence where each term is found by multiplying the position number $ n $ by 4, then subtracting 2.

Q: How do I verify my answer is correct?

Substitute your value of $ n $ back into the original formula. If $ 4n - 2 $ equals 18, you're right!

Arithmetic Sequences with Term Position Finding

Given a formula with a constant property that depends on $n$ :

$4n-2$

Is the number 18 Is it part of the series? If so, what element is it in the series?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's figure out if 8 is part of this sequence. And if so, at what position?

00:16 To find out, we'll plug 8 into our sequence formula and solve it.

00:22 If we get a positive whole number for N, then 8 is in the sequence at position N.

00:27 Okay, let's work to isolate the variable N now.

00:50 And there we go. That's how we solve this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given a formula with a constant property that depends on $n$ :

$4n-2$

Is the number 18 Is it part of the series? If so, what element is it in the series?

Step-by-step solution

To determine if the number 18 is part of the series described by the formula $a_n = 4n - 2$ , follow these steps:

Step 1: Set up the equation $4n - 2 = 18$ .
Step 2: Solve for $n$ by first adding 2 to both sides: $4n = 20$ .
Step 3: Divide both sides by 4 to isolate $n$ : $n = 5$ .

We have found $n = 5$ , which is an integer, indicating that 18 is indeed part of the series $4n - 2$ , where $n$ is a positive integer. Thus, the element 18 is in the 5th position of the series.

Therefore, the number 18 is part of the series, and it is the 5th element.

The correct answer, based on the choices provided, is: Yes, $5$ .

Final Answer

Yes, $5$

Key Points to Remember

Essential concepts to master this topic

Formula: Set sequence formula equal to given value to find position
Technique: Solve $4n - 2 = 18$ gives $n = 5$
Check: Substitute back: $4(5) - 2 = 20 - 2 = 18$ ✓

Common Mistakes

Avoid these frequent errors

Solving the equation incorrectly by not isolating n properly
Don't just guess values or skip algebraic steps = wrong position! This leads to identifying the wrong term number in the sequence. Always solve systematically: add 2 to both sides first, then divide by 4.

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 if I get a decimal or fraction for n?

If $n$ is not a positive integer, then the number is not part of the sequence! Term positions must be whole numbers like 1, 2, 3, etc.

How do I know if 18 is actually in the sequence?

Solve the equation $4n - 2 = 18$ . If you get a positive integer for $n$ , then 18 is the nth term of the sequence.

Can I just substitute different values of n until I find 18?

You could, but it's much faster to solve algebraically! Plus, if the number isn't in the sequence, you'd waste time guessing forever.

What does the formula 4n-2 actually mean?

It's an arithmetic sequence where each term is found by multiplying the position number $n$ by 4, then subtracting 2.

How do I verify my answer is correct?

Substitute your value of $n$ back into the original formula. If $4n - 2$ equals 18, you're right!

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