Question
Justin made 2 phone calls on Friday, 6 phone calls on Saturday, 18 phone calls on Sunday, and 54 phone calls on Monday. What kind of sequence is this?
Answers
GPT-4o mini
To determine the type of sequence represented by the number of phone calls Justin made on different days, let's first list the numbers of phone calls he made:
- Friday: 2
- Saturday: 6
- Sunday: 18
- Monday: 54
Now let's look for a pattern in how each number relates to the previous one.
If we observe the ratio of consecutive terms:
- From Friday to Saturday: \( \frac{6}{2} = 3 \)
- From Saturday to Sunday: \( \frac{18}{6} = 3 \)
- From Sunday to Monday: \( \frac{54}{18} = 3 \)
Each day, the number of phone calls is multiplied by 3.
Thus, the sequence can be represented by the formula:
\[ a_n = 2 \cdot 3^{n-1} \]
where \( n \) represents the day of the week starting from 1 (e.g., Friday = 1, Saturday = 2, Sunday = 3, Monday = 4).
Overall, this is a geometric sequence with a starting term of 2 and a common ratio of 3.
- Friday: 2
- Saturday: 6
- Sunday: 18
- Monday: 54
Now let's look for a pattern in how each number relates to the previous one.
If we observe the ratio of consecutive terms:
- From Friday to Saturday: \( \frac{6}{2} = 3 \)
- From Saturday to Sunday: \( \frac{18}{6} = 3 \)
- From Sunday to Monday: \( \frac{54}{18} = 3 \)
Each day, the number of phone calls is multiplied by 3.
Thus, the sequence can be represented by the formula:
\[ a_n = 2 \cdot 3^{n-1} \]
where \( n \) represents the day of the week starting from 1 (e.g., Friday = 1, Saturday = 2, Sunday = 3, Monday = 4).
Overall, this is a geometric sequence with a starting term of 2 and a common ratio of 3.