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

00:07 Let's find the fifth term in the sequence.

00:11 First, determine the location of the term based on the given infor mation.

00:18 Next, plug this position into the formula to solve and find the term .

00:24 Remember, always do multiplication and division before addition and subtraction.

00:30 And that's how we find the solution to this 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

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'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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