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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
- Arithmetic Sequence Check: An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the previous term. To determine if this is an arithmetic sequence, we need to check if the difference between consecutive terms is constant.
- Constant Difference Calculation: The difference between the first and second term is . Similarly, the difference between the second and third term is also . Since the difference is constant, this sequence can be considered an arithmetic sequence with a common difference of .
- Geometric Sequence Check: A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the ratio. To determine if this is a geometric sequence, we need to check if the ratio between consecutive terms is constant.
- Constant Ratio Calculation: The ratio between the first and second term is . Similarly, the ratio between the second and third term is also . Since the ratio is constant, this sequence can be considered a geometric sequence with a common ratio of .
- Arithmetic and Geometric Sequence Conclusion: Since the sequence satisfies the conditions for both an arithmetic sequence (constant difference) and a geometric sequence (constant ratio), the sequence is both an arithmetic and geometric sequence.
