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
00:05 Let's find the seventh term.
00:08 First, substitute the term position, seven, into the formula and solve step by step.
00:24 Remember, always perform multiplication and division before addition and subtraction to get the correct answer.
00:32 And this is how you solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
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

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 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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