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Harper is drawing stars in her notebook. She 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. Harper is drawing stars in her notebook. She 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 Pattern: Identify the pattern in the sequence of stars drawn on each page.Harper draws stars on the first page, stars on the second page, stars on the third page, and stars on the fourth page. To determine the type of sequence, we need to look at the relationship between the numbers.
- Check Arithmetic: Check if the sequence is arithmetic by finding the difference between consecutive terms.The difference between the first and second page is .The difference between the second and third page is .The difference between the third and fourth page is .Since the differences are not the same, the sequence is not arithmetic.
- Check Geometric: Check if the sequence is geometric by finding the ratio between consecutive terms.The ratio between the second and first page is .The ratio between the third and second page is .The ratio between the fourth and third page is .Since the ratios are not the same, the sequence is not geometric.
- Determine Sequence Type: Determine the type of sequence based on the findings from steps and .Since the sequence is neither arithmetic (the differences are not constant) nor geometric (the ratios are not constant), the correct choice is:(D) neither.
