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Ed is drawing stars in his notebook. He draws stars on the first page, stars on the second page, stars on the third page, and stars on the fourth page. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
Full solution
Q. Ed is drawing stars in his notebook. He draws stars on the first page, stars on the second page, stars on the third page, and stars on the fourth page. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Identify Differences: To determine the type of sequence, we need to look at the differences or ratios between consecutive terms.First, let's find the differences between consecutive terms.Difference between the second and the first term: Difference between the third and the second term: Difference between the fourth and the third term:
- Analyzing Differences: Now, let's analyze the differences. If the differences between consecutive terms are constant, it is an arithmetic sequence. If the ratios between consecutive terms are constant, it is a geometric sequence.From the differences calculated in the previous step, we can see that the differences are not constant and ). Therefore, it is not an arithmetic sequence.
- Check Geometric Sequence: Next, let's check if it's a geometric sequence by finding the ratios between consecutive terms.Ratio between the second and the first term: Ratio between the third and the second term: Ratio between the fourth and the third term: We can see that these ratios are not the same without even calculating them because the differences are not constant and are decreasing. Therefore, it is not a geometric sequence.
- Final Conclusion: Since the sequence is neither arithmetic (the differences are not constant) nor geometric (the ratios are not constant), the correct choice is:(D) neither
