Final answer:
The sequence (0, 8, 18, 32, 50, ...) does not have either a constant difference or a constant ratio between terms, so it is neither an arithmetic sequence nor a geometric sequence.
Step-by-step explanation:
To determine the classification of the sequence (0, 8, 18, 32, 50, ...), we must analyze the differences or ratios between terms.
For an arithmetic sequence, the difference between any two consecutive terms is constant. Calculating the differences between terms for this sequence, we have:
- 8 - 0 = 8
- 18 - 8 = 10
- 32 - 18 = 14
- 50 - 32 = 18
The differences are not constant, which means this sequence is not arithmetic.
For a geometric sequence, the ratio between any two consecutive terms should be the same. Let's calculate the ratios:
- 8 / 0 is undefined (we cannot divide by zero)
- 18 / 8 = 2.25
Given the division by zero and the different ratio for the second set of terms, we can say the sequence is not geometric.
Since the sequence is neither arithmetic nor geometric, the correct answer is (c) Neither arithmetic nor geometric.