Question

For each sequence, determine whether it appears to be arithmetic. If it does, find the common difference.

A) 8, 5, 2, -1 (arithmetic common difference d = -3)
B) 4, 8, 16, 32 (arithmetic common difference d = 4)
C) 12, 19, 26, 33 (arithmetic common difference d = 7)

Answer 1

Determining whether a sequence is arithmetic involves finding a constant difference between consecutive terms. Sequence A has a common difference of -3 and is arithmetic, while sequence B is not arithmetic as the differences aren't constant. Sequence C is arithmetic with a common difference of 7.

Step-by-step explanation:

To determine whether each sequence is arithmetic, we need to find the common difference by subtracting any term from the preceding term. If this difference is constant, the sequence is arithmetic. Here are the sequences analyzed:

1. A) 8, 5, 2, -1: Subtract the second term from the first, third from the second, and so on: 5 - 8 = -3, 2 - 5 = -3, -1 - 2 = -3. Since the differences are equal, the sequence is arithmetic with a common difference of d = -3.
2. B) 4, 8, 16, 32: This sequence is not arithmetic because the differences are not constant: 8 - 4 = 4, 16 - 8 = 8, 32 - 16 = 16. Hence, there's no common difference d in this case.
3. C) 12, 19, 26, 33: Subtracting in the same fashion: 19 - 12 = 7, 26 - 19 = 7, 33 - 26 = 7. This sequence is therefore arithmetic with a common difference of d = 7.