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Emma has a garden and likes to put flowers from her garden into pretty vases. Emma put flowers in the first vase, flowers in the second vase, flowers in the third vase, and flowers in the fourth vase. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
Full solution
Q. Emma has a garden and likes to put flowers from her garden into pretty vases. Emma put flowers in the first vase, flowers in the second vase, flowers in the third vase, and flowers in the fourth vase. 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 numbers. We have , , , and . Let's check if the difference between consecutive terms is constant, which would indicate an arithmetic sequence.Difference between second and first term: Difference between third and second term: Difference between fourth and third term: The differences are not constant, so this is not an arithmetic sequence.
- Check for Arithmetic Sequence: Since the sequence is not arithmetic, let's check if each term is a constant multiple of the previous term, which would indicate a geometric sequence.Ratio of second to first term: Ratio of third to second term: Ratio of fourth to third term: The ratio is constant, so this is a geometric sequence.
