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A tennis club charges players a $ 20 court fee, plus a $ 10 hourly charge with a 5 -hour maximum. A posted list of the total charges for 1,2,3,4 , or 5 hours forms an arithmetic sequence. What is the first term and what is the common difference?

Respuesta :

The first term of the arithmetic sequence so formed is $20 and the common difference is $10.

What is arithmetic progression?

A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.

Given:

  • Initial fee charged by players = $20.
  • Hourly charge = $10
  • Maximum number of hours = $5

To find: The first term and common difference of the arithmetic progression so formed.

Finding:

As the initial charge charged by the players is $20, it can be taken as the first term of the arithmetic sequence, at 0 hours; a₁ = 20

Now, since the hourly charge is $10, the given arithmetic sequence of the money charged will increase by $10 per hour; thus d = 10

The arithmetic sequence holds true for 5 hours maximum.

Thus the sequence so formed => [tex]a_n = 20 + (n - 1)10[/tex], 1 ≤ n ≤ 5.

Hence, The first term of the arithmetic sequence so formed is $20 and the common difference is $10.

To learn more about arithmetic Progressions, refer to the link: https://brainly.com/question/6561461

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