Is 10 a Term in the Sequence Defined by n-4?

Q: What if I get a decimal or fraction for n?

If n isn't a positive whole number, then your target value is not a term in the sequence. Sequence positions must be natural numbers (1, 2, 3, ...).

Q: Can I just guess which position it might be?

Never guess! Always solve algebraically by setting $ a_n = \text{your target} $. Guessing wastes time and often leads to wrong answers.

Q: How do I check if my answer is correct?

Substitute your n-value back into the original formula. Here: $ a_{14} = 14 - 4 = 10 $ ✓. If you get your target number, you're right!

Q: What does the sequence n-4 actually look like?

The first few terms are: 1st term: $ 1 - 4 = -3 $2nd term: $ 2 - 4 = -2 $3rd term: $ 3 - 4 = -1 $ So it starts with negative numbers and increases by 1 each time.

Sequence Terms with Position Finding

A sequence has a rule of $n-4$ .

Is the number 10 a term in the sequence?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is the number 10 a member of the sequence?

00:03 Let's substitute the member in the sequence formula and solve for N

00:07 If the solution for N is positive and whole, then this is the position of the member

00:12 Let's isolate N

00:22 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

A sequence has a rule of $n-4$ .

Is the number 10 a term in the sequence?

Step-by-step solution

To determine if 10 is a term in the given sequence $a_n = n-4$ , we need to solve the equation for $n$ .

First, write down the equation based on the rule of the sequence:

$a_n = n-4$

We want to see if $a_n = 10$ , so set the equation equal to 10:

$n-4 = 10$

Next, solve for $n$ by isolating it on one side of the equation. Add 4 to both sides:

$n = 10 + 4$
$n = 14$

This calculation shows that the 14th term in the sequence equals 10.

Therefore, the number 10 is indeed a term in the sequence, specifically the 14th term.

Yes, it is the 14th term.

Final Answer

Yes, it is the 14th term.

Key Points to Remember

Essential concepts to master this topic

Rule: To find if a number is a term, solve $a_n = \text{target value}$
Technique: Set $n - 4 = 10$ and solve to get $n = 14$
Check: Verify by calculating $a_{14} = 14 - 4 = 10$ ✓

Common Mistakes

Avoid these frequent errors

Confusing the position number with the term value
Don't think that 10 must be the 10th term just because it's the number 10! This ignores the sequence rule completely. Always solve the equation by setting the formula equal to your target value to find the correct position.

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

How do I know which term position a number is?

Set the sequence formula equal to your target number and solve for n. In this case: $n - 4 = 10$ , so $n = 14$ . The number 10 is the 14th term!

What if I get a decimal or fraction for n?

If n isn't a positive whole number, then your target value is not a term in the sequence. Sequence positions must be natural numbers (1, 2, 3, ...).

Can I just guess which position it might be?

Never guess! Always solve algebraically by setting $a_n = \text{your target}$ . Guessing wastes time and often leads to wrong answers.

How do I check if my answer is correct?

Substitute your n-value back into the original formula. Here: $a_{14} = 14 - 4 = 10$ ✓. If you get your target number, you're right!

What does the sequence n-4 actually look like?

The first few terms are:

1st term: $1 - 4 = -3$
2nd term: $2 - 4 = -2$
3rd term: $3 - 4 = -1$

So it starts with negative numbers and increases by 1 each time.

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