To determine whether the given sequence \(-7, -4, -1, 2, 5, \ldots\) is arithmetic or geometric, we need to analyze the differences between the consecutive terms.
- Check if the sequence is arithmetic:
- The difference between the first term and the second term: \[ -4 - (-7) = -4 + 7 = 3 \]
- The difference between the second term and the third term: \[ -1 - (-4) = -1 + 4 = 3 \]
- The difference between the third term and the fourth term: \[ 2 - (-1) = 2 + 1 = 3 \]
- The difference between the fourth term and the fifth term: \[ 5 - 2 = 3 \]
Since the difference between all consecutive terms is the same (3), the sequence is an arithmetic sequence.
-
Common Difference: The common difference is \(3\).
-
Next Three Terms: To find the next three terms, we can continue adding the common difference of \(3\):
- Next term after \(5\): \[ 5 + 3 = 8 \]
- Next term after \(8\): \[ 8 + 3 = 11 \]
- Next term after \(11\): \[ 11 + 3 = 14 \]
Thus, the next three terms in the sequence are \(8, 11, 14\).
Summary:
- The sequence is arithmetic.
- It has a common difference of \(3\).
- The common difference is \(3\).
- The next three terms are \(8, 11, 14\).