Calculate the 5th Element Using the Term-to-Term Rule: 2n + 2

Q: What's the difference between a term-to-term rule and an nth term formula?

Great question! A term-to-term rule tells you how to get from one term to the next (like 'add 3'). An nth term formula like $ 2n + 2 $ lets you find any term directly by substituting the position number.

Q: Why do I substitute n = 5 instead of adding something 5 times?

Because $ 2n + 2 $ is a direct formula! The variable n represents the position number. For the 5th term, simply replace n with 5 and calculate.

Q: What if I get confused about which number to substitute?

Remember: n is always the position number you're looking for. Want the 5th element? Use n = 5. Want the 10th element? Use n = 10. It's that simple!

Q: Can I use this method for any sequence formula?

Absolutely! Whether it's $ 3n - 1 $, $ n^2 + 5 $, or any other nth term formula, just substitute the position number for n and calculate.

Sequence Formulas with Position Substitution

A sequence has the following term-to-term rule:

$2n+2$

What is the value of the 5th 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 5th term in the sequence

00:03 Location of the desired term according to the given data

00:11 Insert the appropriate position in the formula and solve to find the term

00:16 Always solve multiplication and division before addition and subtraction

00:23 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

A sequence has the following term-to-term rule:

$2n+2$

What is the value of the 5th element in the sequence?

Step-by-step solution

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

Step 1: Substitute the position number into the sequence rule.
Step 2: Simplify the expression to find the specific term's value.

Now, let's work through each step:
Step 1: With the term-to-term rule given as $2n + 2$ , we substitute $n = 5$ .
$a_5 = 2(5) + 2$

Step 2: Perform the calculations:
$a_5 = 10 + 2 = 12$

Therefore, the value of the 5th element in the sequence is $12$ .

Final Answer

$12$

Key Points to Remember

Essential concepts to master this topic

Formula: Use the given rule to find any term's value
Technique: Substitute n = 5 into 2n + 2 to get 2(5) + 2
Check: Verify that 10 + 2 = 12 matches the correct answer ✓

Common Mistakes

Avoid these frequent errors

Confusing term-to-term rule with nth term formula
Don't think 2n + 2 means 'add 2n + 2 to the previous term' = wrong sequence! This is actually the nth term formula, not a recursive rule. Always substitute the position number directly into the given expression.

Practice Quiz

Test your knowledge with interactive questions

12 ☐ 10 ☐ 8 7 6 5 4 3 2 1

Which numbers are missing from the sequence so that the sequence has a term-to-term rule?

FAQ

Everything you need to know about this question

What's the difference between a term-to-term rule and an nth term formula?

Great question! A term-to-term rule tells you how to get from one term to the next (like 'add 3'). An nth term formula like $2n + 2$ lets you find any term directly by substituting the position number.

Why do I substitute n = 5 instead of adding something 5 times?

Because $2n + 2$ is a direct formula! The variable n represents the position number. For the 5th term, simply replace n with 5 and calculate.

How can I check if my answer is right?

Try calculating a few other terms! For example, the 1st term: $2(1) + 2 = 4$ , 2nd term: $2(2) + 2 = 6$ . The sequence should increase by 2 each time: 4, 6, 8, 10, 12...

What if I get confused about which number to substitute?

Remember: n is always the position number you're looking for. Want the 5th element? Use n = 5. Want the 10th element? Use n = 10. It's that simple!

Can I use this method for any sequence formula?

Absolutely! Whether it's $3n - 1$ , $n^2 + 5$ , or any other nth term formula, just substitute the position number for n and calculate.

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