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While organizing the magazines at the doctor's office, Percy put magazines in the first pile, magazines in the second pile, magazines in the third pile, and magazines in the fourth pile. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
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Q. While organizing the magazines at the doctor's office, Percy put magazines in the first pile, magazines in the second pile, magazines in the third pile, and magazines in the fourth pile. 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 given: .
- Check Arithmetic Sequence: We can start by checking if it's an arithmetic sequence, which means the difference between consecutive terms should be constant.
- Calculate Differences: Calculate the difference between the second and the first term: .
- Check Geometric Sequence: Calculate the difference between the third and the second term: .
- Calculate Ratios: Calculate the difference between the fourth and the third term: .
- Identify Quadratic Sequence: Since the differences are not constant , it is not an arithmetic sequence.
- Identify Quadratic Sequence: Since the differences are not constant (, , ), it is not an arithmetic sequence.Next, we check if it's a geometric sequence, which means the ratio between consecutive terms should be constant.
- Identify Quadratic Sequence: Since the differences are not constant (, , ), it is not an arithmetic sequence.Next, we check if it's a geometric sequence, which means the ratio between consecutive terms should be constant.Calculate the ratio between the second and the first term: . This does not result in a whole number.
- Identify Quadratic Sequence: Since the differences are not constant (), it is not an arithmetic sequence.Next, we check if it's a geometric sequence, which means the ratio between consecutive terms should be constant.Calculate the ratio between the second and the first term: . This does not result in a whole number.Calculate the ratio between the third and the second term: . This also does not result in a whole number.
- Identify Quadratic Sequence: Since the differences are not constant (), it is not an arithmetic sequence.Next, we check if it's a geometric sequence, which means the ratio between consecutive terms should be constant.Calculate the ratio between the second and the first term: . This does not result in a whole number.Calculate the ratio between the third and the second term: . This also does not result in a whole number.Since the ratios are not constant and not whole numbers, it is not a geometric sequence.
- Identify Quadratic Sequence: Since the differences are not constant (, , ), it is not an arithmetic sequence.Next, we check if it's a geometric sequence, which means the ratio between consecutive terms should be constant.Calculate the ratio between the second and the first term: . This does not result in a whole number.Calculate the ratio between the third and the second term: . This also does not result in a whole number.Since the ratios are not constant and not whole numbers, it is not a geometric sequence.We can observe that the numbers , , , are perfect squares: , , , . This is a different kind of sequence known as a quadratic sequence, which is neither arithmetic nor geometric.
