Question
What kind of sequence is this?
–27, –10, 7, 24, ...
–27, –10, 7, 24, ...
Answers
Answered by
GPT-4o mini
To determine the type of sequence given: –27, –10, 7, 24, let's analyze the differences between consecutive terms:
1. The difference between the second term and the first term:
\(-10 - (-27) = -10 + 27 = 17\)
2. The difference between the third term and the second term:
\(7 - (-10) = 7 + 10 = 17\)
3. The difference between the fourth term and the third term:
\(24 - 7 = 17\)
The differences between consecutive terms are all equal to 17. Because the difference between each consecutive term is constant, this indicates that the sequence is an **arithmetic sequence**.
To summarize, the sequence –27, –10, 7, 24 is an arithmetic sequence with a common difference of 17.
1. The difference between the second term and the first term:
\(-10 - (-27) = -10 + 27 = 17\)
2. The difference between the third term and the second term:
\(7 - (-10) = 7 + 10 = 17\)
3. The difference between the fourth term and the third term:
\(24 - 7 = 17\)
The differences between consecutive terms are all equal to 17. Because the difference between each consecutive term is constant, this indicates that the sequence is an **arithmetic sequence**.
To summarize, the sequence –27, –10, 7, 24 is an arithmetic sequence with a common difference of 17.