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Cindy swam laps on Monday, laps on Tuesday, laps on Wednesday, and laps on Thursday. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
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Q. Cindy swam laps on Monday, laps on Tuesday, laps on Wednesday, and laps on Thursday. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Determine Sequence Type: To determine the type of sequence, we need to look at the pattern of the numbers. We will compare the ratios of consecutive terms to see if they are constant, which would indicate a geometric sequence, or if the differences between consecutive terms are constant, which would indicate an arithmetic sequence.
- Check Arithmetic Sequence: First, let's check if it's an arithmetic sequence by finding the differences between consecutive terms:Difference between Tuesday and Monday: Difference between Wednesday and Tuesday: Difference between Thursday and Wednesday:
- Check Geometric Sequence: We can see that the differences are not constant, as they are doubling each time. This means the sequence is not arithmetic.
- Check Geometric Sequence: We can see that the differences are not constant, as they are doubling each time. This means the sequence is not arithmetic.Now, let's check if it's a geometric sequence by finding the ratios of consecutive terms:Ratio of Tuesday to Monday: Ratio of Wednesday to Tuesday: Ratio of Thursday to Wednesday:
- Check Geometric Sequence: We can see that the differences are not constant, as they are doubling each time. This means the sequence is not arithmetic.Now, let's check if it's a geometric sequence by finding the ratios of consecutive terms:Ratio of Tuesday to Monday: Ratio of Wednesday to Tuesday: Ratio of Thursday to Wednesday: The ratios of consecutive terms are constant, which means the sequence is geometric. Each term is times the previous term.
