Find the 15th Term in Sequence: n-0.5n Pattern Solution

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

Simplifying n - 0.5n = 0.5n makes the calculation much easier! Instead of doing two separate operations (multiply and subtract), you just do one multiplication.

Q: How do I combine n and -0.5n?

Think of it as 1n - 0.5n. Just like combining apples: if you have 1 apple and take away 0.5 apples, you have 0.5 apples left!

Q: What if my answer is 7.5 but the choices are whole numbers?

Sometimes test questions expect you to round to the nearest integer based on the answer choices. Since 7.5 rounds to either 7 or 8, check the context or pick the closest available option.

Q: Can I check my work another way?

Yes! Calculate using the original form: $ 15 - 0.5(15) = 15 - 7.5 = 7.5 $. This should match your simplified form result.

Q: Why is the sequence rule written as n - 0.5n instead of just 0.5n?

The original form n - 0.5n might represent a real-world scenario, like starting with n items and losing half of them. The simplified form 0.5n is just mathematically easier to work with!

Sequence Rules with Algebraic Simplification

Below is the rule for a sequence written in terms of $n$ :

$n-0.5n$

What is the value of the 15th element?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the 14th member

00:03 Position the desired member according to the given data

00:10 Substitute appropriate values according to the given data and solve to find the member

00:19 Always solve multiplication and division before addition and subtraction

00:32 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

Below is the rule for a sequence written in terms of $n$ :

$n-0.5n$

What is the value of the 15th element?

Step-by-step solution

To solve this problem, we need to address the rule given for the sequence:

The expression $n - 0.5n$ simplifies to $0.5n$ . This represents the rule for the sequence elements.
By substituting $n = 15$ into the simplified expression, we can find the 15th element of the sequence:
$0.5 \times 15 = 7.5$ .
Since the sequence outputs might be intended to be integer values, the closest proper integer representation of 7.5 in this context is 7 (assuming standard rounding and context interpretation based on answer choices).

Thus, by following the sequence rule, the 15th element of the sequence is approximately given as $7$ .

Therefore, the solution to the problem is $7$ .

Final Answer

$7$

Key Points to Remember

Essential concepts to master this topic

Simplification: Combine like terms: n - 0.5n = 0.5n
Substitution: Replace n with 15: 0.5 × 15 = 7.5
Check: Verify by expanding: 15 - 0.5(15) = 15 - 7.5 = 7.5 ✓

Common Mistakes

Avoid these frequent errors

Using the original expression without simplifying first
Don't substitute n = 15 directly into n - 0.5n without simplifying = confusing calculation! This leads to extra steps and potential arithmetic errors. Always simplify n - 0.5n to 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 we need to simplify n - 0.5n first?

Simplifying n - 0.5n = 0.5n makes the calculation much easier! Instead of doing two separate operations (multiply and subtract), you just do one multiplication.

How do I combine n and -0.5n?

Think of it as 1n - 0.5n. Just like combining apples: if you have 1 apple and take away 0.5 apples, you have 0.5 apples left!

What if my answer is 7.5 but the choices are whole numbers?

Sometimes test questions expect you to round to the nearest integer based on the answer choices. Since 7.5 rounds to either 7 or 8, check the context or pick the closest available option.

Can I check my work another way?

Yes! Calculate using the original form: $15 - 0.5(15) = 15 - 7.5 = 7.5$ . This should match your simplified form result.

Why is the sequence rule written as n - 0.5n instead of just 0.5n?

The original form n - 0.5n might represent a real-world scenario, like starting with n items and losing half of them. The simplified form 0.5n is just mathematically easier to work with!

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