Calculate 2(n+4): Finding the 9th Element in a Linear Sequence

Q: What does n represent in a sequence formula?

n represents the position in the sequence! If you want the 9th element, then n = 9. If you want the 5th element, then n = 5. It's like a seat number in a row.

Q: Do I always follow order of operations with sequence formulas?

Yes! Always follow PEMDAS/BODMAS. In $ 2(n+4) $, first calculate what's in parentheses (n+4), then multiply by 2.

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

Substitute your n value step by step: n = 9 → 9+4 = 13 → 2×13 = 26. You can also calculate a few other terms to see if the pattern makes sense!

Q: Can sequence formulas have more complex expressions?

Absolutely! You might see formulas like $ n^2 + 3 $ or $ \frac{n}{2} - 1 $. The key is always the same: substitute the position number for n and calculate carefully.

Sequence Formulas with Position Substitution

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

$2(n+4)$

Work out the value of the 9th element in the sequence.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's find the ninth element in the sequence.

00:14 First, identify the position of this element based on the data.

00:19 Then, plug in the appropriate numbers, and solve the equation to find the element.

00:28 Remember, always solve what's inside the parentheses first.

00:37 And there you have it, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

$2(n+4)$

Work out the value of the 9th element in the sequence.

Step-by-step solution

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

Step 1: Understand the sequence rule and identify the variable $n$ .
Step 2: Substitute the value of $n$ into the sequence formula.
Step 3: Calculate the value of the expression obtained.

Let's work through them:
Step 1: The sequence is defined by the rule $2(n+4)$ . Here, $n$ is the position in the sequence since we are asked for the 9th element, $n = 9$ .
Step 2: Substitute $n = 9$ into the expression, which gives us $2(9+4)$ .
Step 3: Calculate $9 + 4$ to get 13. Then multiply by 2 to obtain $2 \times 13 = 26$ .

Thus, the value of the 9th element in the sequence is $26$ .

Final Answer

$26$

Key Points to Remember

Essential concepts to master this topic

Rule: Replace n with the position number in the sequence formula
Technique: For 9th element: substitute n = 9 into 2(n+4)
Check: Work order of operations: 2(9+4) = 2(13) = 26 ✓

Common Mistakes

Avoid these frequent errors

Using the wrong value for n
Don't use the formula value as n or confuse position with term value = wrong substitution! Students often substitute 26 or 2 instead of 9. Always use the position number (9th element means n = 9) in the sequence formula.

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 a sequence formula?

n represents the position in the sequence! If you want the 9th element, then n = 9. If you want the 5th element, then n = 5. It's like a seat number in a row.

Do I always follow order of operations with sequence formulas?

Yes! Always follow PEMDAS/BODMAS. In $2(n+4)$ , first calculate what's in parentheses (n+4), then multiply by 2.

How can I check if my sequence answer is correct?

Substitute your n value step by step: n = 9 → 9+4 = 13 → 2×13 = 26. You can also calculate a few other terms to see if the pattern makes sense!

What if I get a decimal or fraction in my sequence?

That's completely normal! Sequences can have any type of numbers. Just make sure you're substituting correctly and following order of operations.

Can sequence formulas have more complex expressions?

Absolutely! You might see formulas like $n^2 + 3$ or $\frac{n}{2} - 1$ . The key is always the same: substitute the position number for n and calculate carefully.

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