Read the story and respond to the requests below.

Question

Leo has $465 in a savings account. After one month, he has $530 in the account. The next month, the balance is $595. The balance after the third month is $660.

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

The sequence represented by the story is:

1. $465 (initial amount)
2. $530 (after one month)
3. $595 (after two months)
4. $660 (after three months)

To identify whether the sequence is arithmetic or geometric, we will check the differences between consecutive terms:

• From $465 to $530: $530 - $465 = $65
• From $530 to $595: $595 - $530 = $65
• From $595 to $660: $660 - $595 = $65

Since the differences between consecutive terms are the same ($65), this is an arithmetic sequence.

Now, we can identify that there is a common difference in this sequence.

The common difference is $65.

To find the next three terms, we will add the common difference of $65 to the last term ($660):

1. Next term: $660 + $65 = $725
2. Next term: $725 + $65 = $790
3. Next term: $790 + $65 = $855

Therefore, the next three terms are:

• $725
• $790
• $855