Question

In a given year, two tennis academies each had 120 players who went on to play professionally. In the following years, the number of players who wer on to play professionally from academy A increased by 10 players every year. The number of players who went on to play professionally from academy B increased by 10% every year. Use the given information to complete the sentence.

The number of players who went on to play professionally at ______can be represented by _________sequence because the numbers of players who went on to play professionally in successive years have a common _______of 10

Answer 1

The number of players who went on to play professionally at academy A can be represented by an arithmetic sequence with a common difference of 10. The number of players at academy B can be represented by a geometric sequence with a common ratio of 10%.

Step-by-step explanation:

The number of players who went on to play professionally at academy A can be represented by an arithmetic sequence because the numbers of players who went on to play professionally in successive years have a common difference of 10. The sequence can be written as:

An = 120 + 10n, where n represents the number of years since the given year.

On the other hand, the number of players who went on to play professionally at academy B can be represented by a geometric sequence because the numbers of players who went on to play professionally in successive years have a common ratio of 10%. The sequence can be written as:

Bn = 120(1 + 0.10)n, where n represents the number of years since the given year.