Let's define the sequence based on the balances in Leonardo's savings account at the end of each month:
- After the first month: $580
- After the second month: $635
- After the third month: $690
Thus, the sequence starts from $525 and goes as follows:
- First term: 525
- Second term: 580
- Third term: 635
- Fourth term: 690
The sequence can be represented as: \( 525, 580, 635, 690 \)
Is the sequence arithmetic or geometric?
The sequence is arithmetic because the difference between consecutive terms is constant.
Common difference or common ratio?
In this case, since the sequence is arithmetic, we have a common difference.
What is the common difference?
To find the common difference, we can subtract the first term from the second term:
- \( 580 - 525 = 55 \)
- \( 635 - 580 = 55 \)
- \( 690 - 635 = 55 \)
So, the common difference is \( 55 \).
Next three terms?
To find the next three terms in the sequence, we can continue adding the common difference of \( 55 \):
- Fifth term: \( 690 + 55 = 745 \)
- Sixth term: \( 745 + 55 = 800 \)
- Seventh term: \( 800 + 55 = 855 \)
Thus, the next three terms are \( 745, 800, 855 \).
Summary
- Sequence: \( 525, 580, 635, 690 \)
- Type: Arithmetic
- Common difference: \( 55 \)
- Next three terms: \( 745, 800, 855 \)