To identify the type of sequence provided, let's look at the differences between consecutive terms:
-
The difference between the second term and the first term: \(-115 - (-133) = -115 + 133 = 18\)
-
The difference between the third term and the second term: \(-96 - (-115) = -96 + 115 = 19\)
-
The difference between the fourth term and the third term: \(-76 - (-96) = -76 + 96 = 20\)
We can observe that the differences are increasing by 1 each time:
- The difference from the first to the second term is \(18\).
- The difference from the second to the third term is \(19\).
- The difference from the third to the fourth term is \(20\).
Thus, this sequence is not a simple arithmetic sequence (where the difference between terms is constant), but it follows a pattern where the difference between consecutive terms increases linearly.
This is an example of a quadratic sequence, where the second differences (the differences of the differences) are constant. In this case, the first differences are increasing by \(1\) each time, meaning that the second differences are constant (\(1\)).
Therefore, the sequence is a quadratic sequence.