Calculate the 11th Term in the Sequence 2n+2: Step-by-Step Solution

Q: What does 'n' represent in the formula 2n+2?

The variable n represents the position of the term in the sequence. So n=1 gives the 1st term, n=2 gives the 2nd term, and n=11 gives the 11th term.

Q: Why do I multiply by 2 first, then add 2?

Follow the order of operations (PEMDAS)! Multiplication comes before addition, so calculate $ 2 \times 11 = 22 $ first, then add 2 to get 24.

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

Remember: you're looking for the 11th term, so substitute n=11. The question asks for a specific position in the sequence, not a specific value.

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

Yes! Whether the formula is 3n+1, n², or 5n-7, always substitute the position number for n to find that term's value.

Arithmetic Sequences with Substitution Method

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

$2n+2$

Calculate the value of the 11th element.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the 11th element

00:03 Position of the desired element according to the data

00:11 Substitute appropriate values according to the data and solve to find the element

00:18 Always solve multiplication and division before addition and subtraction

00:25 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

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

$2n+2$

Calculate the value of the 11th element.

Step-by-step solution

We calculate by replacing $n=11$

$2\times11+2=$

First we solve the multiplication exercise and then we add 2:

$22+2=24$

Final Answer

$24$

Key Points to Remember

Essential concepts to master this topic

Rule: Substitute the term position directly into the formula
Technique: For n=11 in 2n+2: calculate 2(11)+2 = 24
Check: Verify by calculating 2×11+2 step by step = 22+2 = 24 ✓

Common Mistakes

Avoid these frequent errors

Confusing term position with term value
Don't substitute the 11th term's value back into the formula = circular reasoning! The 11th term IS what we're trying to find. Always substitute the position number (n=11) into the given formula 2n+2.

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 does 'n' represent in the formula 2n+2?

The variable n represents the position of the term in the sequence. So n=1 gives the 1st term, n=2 gives the 2nd term, and n=11 gives the 11th term.

Why do I multiply by 2 first, then add 2?

Follow the order of operations (PEMDAS)! Multiplication comes before addition, so calculate $2 \times 11 = 22$ first, then add 2 to get 24.

How can I check if my sequence formula is working correctly?

Calculate the first few terms! For 2n+2: when n=1 you get 4, n=2 gives 6, n=3 gives 8. Notice each term increases by 2, which matches the coefficient of n.

What if I get confused about which number to substitute?

Remember: you're looking for the 11th term, so substitute n=11. The question asks for a specific position in the sequence, not a specific value.

Can I use this same method for any sequence formula?

Yes! Whether the formula is 3n+1, n², or 5n-7, always substitute the position number for n to find that term's value.

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