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Answer :
To solve the problem of determining which formula models the cost of buying video games under the conditions given, let's break it down step by step.
1. Understand the Cost Structure:
- The cost of the first video game is [tex]$40.
- Any subsequent game costs $[/tex]25 each.
2. Define the Total Cost for 'n' Games:
- If you buy only one game (the first one), it'll cost you [tex]$40, as there are no additional games yet.
- For any additional games, each one will add $[/tex]25 to the total cost.
3. Formula Derivation:
- The cost of the first game is a fixed [tex]$40.
- For the remaining games, you will buy (n-1) additional games at $[/tex]25 each.
- Therefore, the additional cost for these (n-1) games is [tex]\((n-1) \times 25\)[/tex].
4. Combine Both Costs:
- To find the total cost [tex]\(a_n\)[/tex] for 'n' games, you add the cost of the first game ($40) and the cost of the additional (n-1) games.
- This results in the formula:
[tex]\[
a_n = 40 + (n-1) \times 25
\][/tex]
So, the formula models the total cost of buying 'n' games with the given pricing structure as [tex]\(a_n = 40 + (n-1) \times 25\)[/tex].
1. Understand the Cost Structure:
- The cost of the first video game is [tex]$40.
- Any subsequent game costs $[/tex]25 each.
2. Define the Total Cost for 'n' Games:
- If you buy only one game (the first one), it'll cost you [tex]$40, as there are no additional games yet.
- For any additional games, each one will add $[/tex]25 to the total cost.
3. Formula Derivation:
- The cost of the first game is a fixed [tex]$40.
- For the remaining games, you will buy (n-1) additional games at $[/tex]25 each.
- Therefore, the additional cost for these (n-1) games is [tex]\((n-1) \times 25\)[/tex].
4. Combine Both Costs:
- To find the total cost [tex]\(a_n\)[/tex] for 'n' games, you add the cost of the first game ($40) and the cost of the additional (n-1) games.
- This results in the formula:
[tex]\[
a_n = 40 + (n-1) \times 25
\][/tex]
So, the formula models the total cost of buying 'n' games with the given pricing structure as [tex]\(a_n = 40 + (n-1) \times 25\)[/tex].
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