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Read the story and respond to the requests below.

You begin doing 20 push-ups every day in April. You do 32 push-ups every day in May, 44 push-ups every day in June, and so on.

Write the sequence represented by the story.
Is the sequence arithmetic or geometric?
Does it have a common difference or common ratio?
What is the common difference or common ratio?
What are the next three terms?

1 answer

The sequence represented by the story is as follows:

  • April: 20 push-ups
  • May: 32 push-ups
  • June: 44 push-ups

To see the pattern, we observe the number of push-ups done each month:

  • April: 20
  • May: 32
  • June: 44

The increases are as follows:

  • From April to May: 32 - 20 = 12
  • From May to June: 44 - 32 = 12

So, the sequence can be written as: 20, 32, 44, ...

Is the sequence arithmetic or geometric?

The sequence is arithmetic because the difference between consecutive terms is constant.

Does it have a common difference or common ratio?

It has a common difference.

What is the common difference or common ratio?

The common difference is 12 (the increase from one term to the next).

What are the next three terms?

To find the next three terms, we continue adding the common difference (12) to the last term.

  • Next term after June: 44 + 12 = 56
  • Next term after that: 56 + 12 = 68
  • Next term after that: 68 + 12 = 80

Thus, the next three terms in the sequence are 56, 68, and 80.