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While at work, Arianna is putting papers into folders. She put papers in the first folder, papers in the second folder, papers in the third folder, and papers in the fourth folder. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
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Q. While at work, Arianna is putting papers into folders. She put papers in the first folder, papers in the second folder, papers in the third folder, and papers in the fourth folder. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Identify Pattern: First, let's identify the pattern in the sequence of numbers representing the papers put into each folder: . To determine if it's an arithmetic sequence, we need to check if the difference between consecutive terms is constant. Difference between the second and the first term: Difference between the third and the second term: Difference between the fourth and the third term:
- Check Arithmetic Sequence: Since the difference between each pair of consecutive terms is the same (), we can conclude that the sequence is arithmetic.An arithmetic sequence is defined by having a constant difference between consecutive terms, which we have confirmed for this sequence.
- Confirm Arithmetic Sequence: Now, let's check if it could also be a geometric sequence by finding the ratio between consecutive terms.However, we can see that the ratio between the second and the first term is not the same as the ratio between the third and the second term , and so on.Therefore, it is not a geometric sequence, as a geometric sequence requires a constant ratio between consecutive terms.
