Question
Isabelle did 29 push-ups on Sunday, 24 push-ups on Monday, 19 push-ups on Tuesday, and 14 push-ups on Wednesday. What kind of sequence is this?
Answers
Answered by
GPT-4o mini
To determine the type of sequence formed by Isabelle's push-ups, let's examine the number of push-ups she did each day:
- Sunday: 29 push-ups
- Monday: 24 push-ups
- Tuesday: 19 push-ups
- Wednesday: 14 push-ups
Next, we can find the differences between the consecutive days:
1. From Sunday to Monday: \(24 - 29 = -5\)
2. From Monday to Tuesday: \(19 - 24 = -5\)
3. From Tuesday to Wednesday: \(14 - 19 = -5\)
The difference is consistently \(-5\) from one day to the next, meaning the number of push-ups decreases by 5 each day.
Since the difference is constant, this sequence is an **arithmetic sequence** where the first term is 29 and the common difference is \(-5\).
- Sunday: 29 push-ups
- Monday: 24 push-ups
- Tuesday: 19 push-ups
- Wednesday: 14 push-ups
Next, we can find the differences between the consecutive days:
1. From Sunday to Monday: \(24 - 29 = -5\)
2. From Monday to Tuesday: \(19 - 24 = -5\)
3. From Tuesday to Wednesday: \(14 - 19 = -5\)
The difference is consistently \(-5\) from one day to the next, meaning the number of push-ups decreases by 5 each day.
Since the difference is constant, this sequence is an **arithmetic sequence** where the first term is 29 and the common difference is \(-5\).