Solve n-0.5n Sequence: Finding Position of Number 5

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

Simplifying combines like terms and makes the equation much easier to solve! $ n - 0.5n $ becomes $ 0.5n $, which is simpler to work with.

Q: How do I solve 0.5n = 5?

Divide both sides by 0.5 (or multiply by 2): $ n = \frac{5}{0.5} = 10 $. Remember that dividing by 0.5 is the same as multiplying by 2!

Q: What if the number isn't in the sequence?

If solving the equation gives a non-integer value for n (and the sequence only uses whole number positions), then the number isn't in the sequence. Always check if your answer makes sense!

Linear Equations with Position Finding

Given a formula with a constant property that depends on $n$ :

$n-0.5n$

Is the number 5 Is it part of the series? If so, what element is it in the series?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Is the number 5 in this sequence? If it is, where is it?

00:15 To find out, we'll plug 5 into the sequence formula and solve it.

00:20 If we get a positive whole number for N, then 5 is at position N.

00:25 Next, let's focus on isolating N to solve for it.

00:37 And that's how we find the solution. Great job following along!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given a formula with a constant property that depends on $n$ :

$n-0.5n$

Is the number 5 Is it part of the series? If so, what element is it in the series?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Simplify the expression $n - 0.5n$ .
Step 2: Set up the equation for 5 using the simplified formula.
Step 3: Solve for $n$ .
Step 4: Verify the solution.

Now, let's work through each step:
Step 1: Given the expression $n - 0.5n$ , it simplifies to $0.5n$ .
Step 2: Set up the equation $0.5n = 5$ .
Step 3: Solve for $n$ :
To find $n$ , we multiply both sides of the equation by 2:
$n = 10$ .
Step 4: Verification:
Substitute $n = 10$ back into the simplified formula: $0.5 \cdot 10 = 5$ , which confirms that 5 is part of the sequence.

Therefore, the number 5 is indeed part of the sequence, and it corresponds to $n = 10$ .

Yes, $10$

Final Answer

Yes, $10$

Key Points to Remember

Essential concepts to master this topic

Simplification: Combine like terms first: n - 0.5n = 0.5n
Technique: Set simplified expression equal to target: 0.5n = 5
Verification: Substitute back: 0.5(10) = 5 confirms position 10 ✓

Common Mistakes

Avoid these frequent errors

Not simplifying the expression first
Don't try to solve n - 0.5n = 5 directly without combining terms = complex unnecessary work! This makes the problem harder and increases error chances. Always combine like terms first to get 0.5n = 5.

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 combines like terms and makes the equation much easier to solve! $n - 0.5n$ becomes $0.5n$ , which is simpler to work with.

What does 'position in the sequence' mean here?

The position is the value of n that produces our target number. When $n = 10$ , the formula gives us 5, so 5 appears at position 10 in the sequence.

How do I solve 0.5n = 5?

Divide both sides by 0.5 (or multiply by 2): $n = \frac{5}{0.5} = 10$ . Remember that dividing by 0.5 is the same as multiplying by 2!

What if the number isn't in the sequence?

If solving the equation gives a non-integer value for n (and the sequence only uses whole number positions), then the number isn't in the sequence. Always check if your answer makes sense!

Can I check my answer a different way?

Yes! Calculate the first few terms of the sequence: when n=1: 0.5, n=2: 1, n=3: 1.5... You can see the pattern and verify that $n=10$ gives $0.5(10) = 5$ .

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