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There is a sale on video games. The first game you buy will cost [tex]\$40[/tex]. Each game after that will cost [tex]\$25[/tex]. Which formula models this situation?

A. [tex]a_n = (n-1) \times 40[/tex]

B. [tex]a_n = 25 + (n-1) \times 40[/tex]

C. [tex]a_n = 40 + (n-1) \times 25[/tex]

D. [tex]a_n = 65 + (n-1) \times 40[/tex]

Answer :

To solve the problem of determining a formula that models the cost of buying video games during a sale, follow these steps:

1. Understand the Pricing Model:
- The cost of the first video game is [tex]$40.
- Each additional video game costs $[/tex]25.

2. Define the Variable:
- Let [tex]\( n \)[/tex] be the total number of video games you buy.

3. Develop the Formula:
- If you buy just one game ([tex]\( n = 1 \)[/tex]), the cost is [tex]$40.
- If you buy more than one game, you pay $[/tex]40 for the first game and [tex]$25 for each of the remaining \( n-1 \) games.

4. Formulate the Expression:
- The cost for the first game is $[/tex]40.
- The cost for the additional [tex]\( n-1 \)[/tex] games is [tex]\((n-1) \times 25\)[/tex].
- Add these two parts together to get the total cost:
[tex]\[ a_n = 40 + (n-1) \times 25 \][/tex]

This formula will give you the total cost of buying [tex]\( n \)[/tex] video games during the sale.

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