Derek is reviewing his cell phone bill. When he gets to the text message part, he notices that he sent 100 text messages in August, 121 text messages in September, 144 text messages in October, and 169 text messages in November. What kind of sequence is this?

Answer 1

To determine the kind of sequence Derek's text messages form, we can analyze the number of messages he sent each month:

• August: 100
• September: 121
• October: 144
• November: 169

Now let's look at the differences between consecutive terms:

• September - August: 121 - 100 = 21
• October - September: 144 - 121 = 23
• November - October: 169 - 144 = 25

Now let's look at the differences we calculated:

• 21, 23, 25

Next, we will find the differences of these first differences to see if there's a pattern:

• 23 - 21 = 2
• 25 - 23 = 2

The second differences are constant (both equal to 2). This indicates that the original sequence is a quadratic sequence because the second differences are constant.

In conclusion, the sequence of Derek's text messages forms a quadratic sequence.