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Frank bagged the plastic bottles after a recycling drive. He placed bottles in the first bag, bottles in the second bag, bottles in the third bag, and bottles in the fourth bag. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
Full solution
Q. Frank bagged the plastic bottles after a recycling drive. He placed bottles in the first bag, bottles in the second bag, bottles in the third bag, and bottles in the fourth bag. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Find Differences: To determine the type of sequence, we need to look at the differences or ratios between the terms. Let's start by finding the differences between consecutive terms.First difference: Second difference: Third difference:
- Identify Arithmetic Sequence: Since the differences between consecutive terms are all the same (), this indicates that the sequence is an arithmetic sequence.
- Check Geometric Sequence: An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant common difference to the previous term. In this case, the common difference is .
- Sequence Type Determination: Now, let's check if it could also be a geometric sequence by finding the ratios between consecutive terms.First ratio: (this does not simplify to a whole number)Second ratio: (this does not simplify to a whole number)Third ratio: (this does not simplify to a whole number)
- Sequence Type Determination: Now, let's check if it could also be a geometric sequence by finding the ratios between consecutive terms.First ratio: (this does not simplify to a whole number)Second ratio: (this does not simplify to a whole number)Third ratio: (this does not simplify to a whole number)Since the ratios between consecutive terms are not constant, the sequence is not a geometric sequence.
