Question

Which of the following arithmetic sequences have a common difference of 21?

A. 1.5, 22.5, 43.5, 64.5, 85.5
B. 0, -21, -42, -63, -84
C. 3, 24, 45, 66, 87
D. -2, 19, 40, 61, 82

Answer 1

The arithmetic sequences A, C, and D have a common difference of 21.

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. To determine which of the given sequences have a common difference of 21, we need to check if the difference between consecutive terms is 21 for each sequence.

1. Sequence A: The difference between consecutive terms is 22.5 - 1.5 = 21, so this sequence has a common difference of 21.
2. Sequence B: The difference between consecutive terms is -21 - 0 = -21, so this sequence has a common difference of -21, not 21.
3. Sequence C: The difference between consecutive terms is 24 - 3 = 21, so this sequence has a common difference of 21.
4. Sequence D: The difference between consecutive terms is 19 - (-2) = 21, so this sequence has a common difference of 21.

Therefore, the arithmetic sequences A, C, and D have a common difference of 21.