Solve n-0.5n: Finding the 8th Element in a Linear Sequence

Q: Why do I need to simplify n - 0.5n first?

Simplifying reduces calculation errors and makes the pattern clearer! $ n - 0.5n = 0.5n $ shows this is simply "half of the position number."

Q: Is n - 0.5n the same as 0.5n?

Yes! Think of it as taking away half of something leaves you with half remaining. So $ n - 0.5n = 0.5n $.

Q: What if the term number was different, like n = 10?

The same rule applies! For the 10th term: $ 0.5 \times 10 = 5 $. The pattern is always half the position number.

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

Substitute back into the original rule: $ 8 - 0.5(8) = 8 - 4 = 4 $. If this matches your simplified calculation, you're right!

Q: Can I write 0.5n as a fraction instead?

Absolutely! $ 0.5n = \frac{1}{2}n $, so the 8th term is $ \frac{1}{2} \times 8 = \frac{8}{2} = 4 $.

Algebraic Simplification with Term Position Rules

A sequence has a term-to-term rule of $n-0.5n$ .

What is the 8th element of the sequence?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the 8th element in the sequence

00:03 Location of the desired element according to the given data

00:09 Substitute the appropriate position in the formula and solve to find the element

00:17 Always solve multiplication and division before addition and subtraction

00:24 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 term-to-term rule of $n-0.5n$ .

What is the 8th element of the sequence?

Step-by-step solution

To find the 8th element of this sequence, we must apply the given term-to-term rule:

The rule provided is $n - 0.5n$ . Simplifying this, we obtain:

$n - 0.5n = 0.5n$

Thus, for the 8th term, substitute $n = 8$ into the simplified rule:

$0.5 \times 8 = 4$

Therefore, the 8th element of the sequence is $4$ .

Thus, the correct answer is choice 1: $4$ .

Final Answer

$4$

Key Points to Remember

Essential concepts to master this topic

Simplification: Combine like terms first: n - 0.5n = 0.5n
Substitution: Replace n with position number: 0.5 × 8 = 4
Verification: Check by expanding: 8 - 0.5(8) = 8 - 4 = 4 ✓

Common Mistakes

Avoid these frequent errors

Using the unsimplified rule directly
Don't substitute n = 8 into n - 0.5n without simplifying first = 8 - 0.5(8) = extra steps and confusion! Students often make arithmetic errors with this longer calculation. Always simplify n - 0.5n = 0.5n first, then substitute.

Practice Quiz

Test your knowledge with interactive questions

Is there a term-to-term rule for the sequence below?

18 , 22 , 26 , 30

FAQ

Everything you need to know about this question

Why do I need to simplify n - 0.5n first?

Simplifying reduces calculation errors and makes the pattern clearer! $n - 0.5n = 0.5n$ shows this is simply "half of the position number."

Is n - 0.5n the same as 0.5n?

Yes! Think of it as taking away half of something leaves you with half remaining. So $n - 0.5n = 0.5n$ .

What if the term number was different, like n = 10?

The same rule applies! For the 10th term: $0.5 \times 10 = 5$ . The pattern is always half the position number.

How do I check if my answer is correct?

Substitute back into the original rule: $8 - 0.5(8) = 8 - 4 = 4$ . If this matches your simplified calculation, you're right!

Can I write 0.5n as a fraction instead?

Absolutely! $0.5n = \frac{1}{2}n$ , so the 8th term is $\frac{1}{2} \times 8 = \frac{8}{2} = 4$ .

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