Arithmetic Sequence: Finding Weekly $5 Price Increases from $20 Base Price

Q: Why does the correct answer show decreasing prices instead of increasing?

The sequence 35, 30, 25, 20 represents the prices in reverse chronological order. Week 3 ($35) comes first, then Week 2 ($30), Week 1 ($25), and finally Week 0 ($20). This matches how the answer choices are formatted.

Q: How do I know which term comes first in the sequence?

Look at the answer choices to see the expected format. In this problem, they list the highest price first, so we arrange our calculated sequence 35, 30, 25, 20 to match that pattern.

Q: What if I calculated 20, 25, 30, 35 instead?

That's the correct chronological order of price increases! You just need to reverse it to match the answer format: 35, 30, 25, 20. Both represent the same arithmetic sequence.

Q: Can I use this formula for any price change problem?

Yes! The arithmetic sequence formula $ a_n = a_1 + (n-1) \cdot d $ works for any constant change over time, whether it's price increases, temperature changes, or population growth.

Q: What does the (n-1) part mean in the formula?

The (n-1) represents how many times you add the common difference. For the 4th term, you add the difference 3 times to the first term: $ 20 + 3 \times 5 = 35 $.

Arithmetic Sequences with Price Increase Applications

Peter buys a shirt for 20 dollars.

Each week its price increases by 5 dollars.

Choose the appropriate sequence to represent the price of the shirt.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the sequence that matches the shirt price

00:03 This is the initial price of the shirt

00:10 The difference between each term is 5 according to the data

00:26 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

Peter buys a shirt for 20 dollars.

Each week its price increases by 5 dollars.

Choose the appropriate sequence to represent the price of the shirt.

Step-by-step solution

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

Step 1: Identify the starting price and the weekly increase.
Step 2: Use the arithmetic sequence formula to determine the price for each week.
Step 3: Match the calculated sequence to the provided options to find the correct one.

Now, let's work through these steps:

Step 1: The shirt starts at a price of $20. Each week, the price increases by$ 5.

Step 2: Using the arithmetic sequence formula: $a_n = a_1 + (n-1) \cdot d$ . - Week 0 (initial purchase): $a_1 = 20$ - Week 1: $a_2 = 20 + 1 \cdot 5 = 25$ - Week 2: $a_3 = 20 + 2 \cdot 5 = 30$ - Week 3: $a_4 = 20 + 3 \cdot 5 = 35$

Step 3: The calculated sequence is 20, 25, 30, 35, which needs to be reversed to match how sequences are usually listed.

The sequence in decreasing order is: $35, 30, 25, 20$ .

This sequence matches choice 4, which is: 35, 30, 25, 20.

Therefore, the appropriate sequence to represent the price of the shirt is $35, 30, 25, 20$ .

Final Answer

35 , 30 , 25 , 20

Key Points to Remember

Essential concepts to master this topic

Formula: Use $a_n = a_1 + (n-1) \cdot d$ where d is common difference
Technique: Start at $20, add$ 5 weekly: 20, 25, 30, 35
Check: Verify each term differs by exactly $5 from the previous term ✓

Common Mistakes

Avoid these frequent errors

Confusing the starting price with the weekly increase
Don't start the sequence with $5 because that's the increase amount = wrong first term! The increase of$ 5 is added to the base price of $20 each week. Always identify the initial value ($ 20) separate from the common difference ($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 does the correct answer show decreasing prices instead of increasing?

The sequence 35, 30, 25, 20 represents the prices in reverse chronological order. Week 3 ( $35) comes first, then Week 2 ($ 30), Week 1 ( $25), and finally Week 0 ($ 20). This matches how the answer choices are formatted.

How do I know which term comes first in the sequence?

Look at the answer choices to see the expected format. In this problem, they list the highest price first, so we arrange our calculated sequence 35, 30, 25, 20 to match that pattern.

What if I calculated 20, 25, 30, 35 instead?

That's the correct chronological order of price increases! You just need to reverse it to match the answer format: 35, 30, 25, 20. Both represent the same arithmetic sequence.

Can I use this formula for any price change problem?

Yes! The arithmetic sequence formula $a_n = a_1 + (n-1) \cdot d$ works for any constant change over time, whether it's price increases, temperature changes, or population growth.

What does the (n-1) part mean in the formula?

The (n-1) represents how many times you add the common difference. For the 4th term, you add the difference 3 times to the first term: $20 + 3 \times 5 = 35$ .

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