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What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
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Q. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Examine Number Pattern: To determine the type of sequence, we need to examine the pattern of the numbers given in the sequence: First, let's check if it's an arithmetic sequence. An arithmetic sequence has a common difference between consecutive terms.We calculate the difference between the second and the first term: .Then, we calculate the difference between the third and the second term: .Since the differences are not the same, it is not an arithmetic sequence.
- Check Arithmetic Sequence: Next, let's check if it's a geometric sequence. A geometric sequence has a common ratio between consecutive terms.We calculate the ratio between the second and the first term: .Then, we calculate the ratio between the third and the second term: .Since is not a multiple of , the ratio is not consistent, and therefore, it is not a geometric sequence.
- Check Geometric Sequence: Since the sequence is neither arithmetic nor geometric, let's consider other patterns. We notice that each term is a square of an integer: , , , , ... This pattern is characteristic of a sequence of perfect squares, which is neither arithmetic nor geometric.
