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Farid is putting stickers in a sticker book. He put stickers on the first page, stickers on the second page, stickers on the third page, and stickers on the fourth page. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
Full solution
Q. Farid is putting stickers in a sticker book. He put stickers on the first page, stickers on the second page, stickers on the third page, and stickers on the fourth page. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Identify Sequence Type: Farid put stickers on each of the four pages. To determine the type of sequence, we need to look at the pattern of the numbers. An arithmetic sequence has a constant difference between consecutive terms, while a geometric sequence has a constant ratio between consecutive terms.
- Constant Difference: Since Farid put the same number of stickers () on each page, the difference between the number of stickers on any two consecutive pages is . This indicates that the sequence has a constant difference.
- Arithmetic Sequence Definition: A constant difference of means that every term in the sequence is the same. This is a characteristic of an arithmetic sequence, where each term is equal to the previous term plus a constant difference. In this case, the constant difference is .
- Constant Ratio Analysis: Since the ratio between consecutive terms would be , which is constant, it might seem that the sequence could also be considered geometric. However, a geometric sequence typically implies that the ratio is not , as a ratio of would simply create a constant sequence, which is a special case of an arithmetic sequence.
- Final Conclusion: Given that the sequence has a constant difference and the ratio between consecutive terms is , the sequence is best described as an arithmetic sequence. Therefore, the correct choice is arithmetic.
