Leonardo has $525 in a savings account. After one month, he has $580 in the account. The next month, the balance is $635. The balance after the third month is $690.

Question

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?

Answer 1

Let's define the sequence based on the balances in Leonardo's savings account at the end of each month:

1. After the first month: $580
2. After the second month: $635
3. 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 \( 55 \):

1. Fifth term: \( 690 + 55 = 745 \)
2. Sixth term: \( 745 + 55 = 800 \)
3. 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: \( 745, 800, 855 \)