Calculate the Seventh Term in the Linear Sequence: 4n - 10

Arithmetic Sequences with Term Substitution

4n−10 4n-10

What is the seventh term in the sequence above?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the 7th term
00:03 Substitute the appropriate term position in the formula and solve
00:19 Always solve multiplication and division before addition and subtraction
00:27 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

4n−10 4n-10

What is the seventh term in the sequence above?

2

Step-by-step solution

To solve for the seventh term in the sequence defined by 4n−10 4n - 10 , we can follow these steps:

  • Step 1: Identify the formula for the sequence: an=4n−10 a_n = 4n - 10 .
  • Step 2: Since we need the seventh term, set n=7 n = 7 .
  • Step 3: Substitute n=7 n = 7 into the formula:

a7=4(7)−10 a_7 = 4(7) - 10

Step 4: Calculate 4×7=28 4 \times 7 = 28 .

Step 5: Subtract 10 from 28:

a7=28−10=18 a_7 = 28 - 10 = 18

Therefore, the seventh term in the sequence is 18\mathbf{18}.

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Final Answer

18

Key Points to Remember

Essential concepts to master this topic
  • Formula: Substitute the position number for n in the general term
  • Technique: For a7 a_7 , substitute n = 7: 4(7)−10=18 4(7) - 10 = 18
  • Check: Verify by computing consecutive terms to confirm pattern consistency ✓

Common Mistakes

Avoid these frequent errors
  • Confusing the term position with the term value
    Don't substitute the wrong number - using 18 instead of 7 gives 4(18)−10=62 4(18) - 10 = 62 ! Students often mix up what n represents (position) versus what the term equals (value). Always substitute the position number (7th term means n = 7) into the formula.

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 4n−10 4n - 10 ?

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n represents the position of the term in the sequence. For the 7th term, n = 7. For the 1st term, n = 1. Think of n as the counting number for which term you want to find.

How do I know this formula gives an arithmetic sequence?

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The formula 4n−10 4n - 10 is linear (no exponents), so it creates an arithmetic sequence. The coefficient of n (which is 4) tells you the common difference between consecutive terms.

What if I need to find which term equals a certain value?

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Set the formula equal to that value and solve for n. For example, if you want to know which term equals 30: 4n−10=30 4n - 10 = 30 , so n=10 n = 10 (the 10th term).

Can the seventh term ever be negative?

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Absolutely! Sequences can have negative terms. If the formula gave a negative result, that would be the correct answer. Always trust your calculation when you substitute correctly.

Should I write out all seven terms to find the seventh?

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No need! That's the beauty of having the general formula. You can jump directly to any term by substituting its position number for n. It saves time and reduces errors.

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