Calculate the 11th Term: Sequence Defined by 4n-2

Arithmetic Sequences with Position Formula

Below is the term-to-term rule for a sequence written in terms of n n :

4n2 4n-2

What is the value of the 11th element in the sequence?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Found the 11th member in the sequence
00:03 The desired member location according to the data
00:09 We'll substitute the appropriate location in the formula and solve for finding the member
00:13 Always solve multiplication and division before addition and subtraction
00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Below is the term-to-term rule for a sequence written in terms of n n :

4n2 4n-2

What is the value of the 11th element in the sequence?

2

Step-by-step solution

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

  • Step 1: Identify the sequence formula and the term number needed.
  • Step 2: Substitute the term number into the sequence formula.
  • Step 3: Perform calculations to get the resultant value.

Now, let's work through each step:
Step 1: The sequence formula is given as 4n2 4n - 2 , and we need the 11th term, so n=11 n = 11 .
Step 2: Substitute n=11 n = 11 into the sequence formula:

4n2=4(11)2 4n - 2 = 4(11) - 2

Step 3: Perform the calculation:

4(11)=44 4(11) = 44 .

Then subtract 2 to get 442=42 44 - 2 = 42 .

Therefore, the value of the 11th element in the sequence is 42 42 .

3

Final Answer

42 42

Key Points to Remember

Essential concepts to master this topic
  • Formula: Substitute position number directly into 4n2 4n-2
  • Technique: For 11th term, calculate 4(11)2=442=42 4(11) - 2 = 44 - 2 = 42
  • Check: Verify by calculating a few terms to confirm pattern ✓

Common Mistakes

Avoid these frequent errors
  • Confusing position number with term value
    Don't think n=11 means the term equals 11! The position number (11) goes INTO the formula, it's not the answer. Always substitute the position number into 4n2 4n-2 to find the actual term value.

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 4n2 4n-2 ?

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n represents the position of the term in the sequence. So for the 11th term, n = 11, for the 5th term, n = 5, and so on.

How do I know if I'm using the right formula?

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Check by calculating the first few terms! For 4n2 4n-2 : 1st term = 4(1)2=2 4(1)-2 = 2 , 2nd term = 4(2)2=6 4(2)-2 = 6 , 3rd term = 4(3)2=10 4(3)-2 = 10 . The sequence should be 2, 6, 10, 14...

What if I get a negative answer?

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That's totally normal! Some sequences have negative terms. Just make sure you follow the order of operations correctly: multiply first, then subtract.

Can I use this formula for any term position?

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Yes! That's the beauty of having a position formula. Whether you want the 1st term, 50th term, or 100th term, just substitute that number for n.

How do I check my answer is correct?

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Calculate a couple terms around your answer to see if the pattern makes sense. For the 11th term = 42, try the 10th term: 4(10)2=38 4(10)-2 = 38 and 12th term: 4(12)2=46 4(12)-2 = 46 . The sequence should increase by 4 each time! ✓

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