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

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.

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 $35, 30, 25, 20$.