While organizing her DVD collection, Erin put 35 DVDs on the first rack, 50 DVDs on the second rack, 65 DVDs on the third rack, and 80 DVDs on the fourth rack. What kind of sequence is this? Choices: (A)arithmetic (B)geometric (C)both (D)neither

Question

While organizing her DVD collection, Erin put 35 DVDs on the first rack, 50 DVDs on the second rack, 65 DVDs on the third rack, and 80 DVDs on the fourth rack. What kind of sequence is this?     Choices: (A)arithmetic (B)geometric (C)both (D)neither

Bytelearn · Accepted Answer

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 rack: 35 DVDs Second rack: 50 DVDs Third rack: 65 DVDs Fourth rack: 80 DVDs Difference between second and first rack: 50 - 35 = 15 Difference between third and second rack: 65 - 50 = 15 Difference between fourth and third rack: 80 - 65 = 15Arithmetic Sequence: Since the differences between consecutive terms are constant, this indicates that the sequence is an arithmetic sequence.Check Geometric Sequence: Now let's check if it could also be a geometric sequence by finding the ratios between consecutive terms. Ratio of second to first rack: 50 / 35 Ratio of third to second rack: 65 / 50 Ratio of fourth to third rack: 80 / 65Calculate Ratios: Calculating the ratios: 50 / 35 ≈ 1.4286 65 / 50 = 1.3 80 / 65 ≈ 1.2308 Since the ratios are not constant, this is not a geometric sequence.Conclusion: Based on the constant differences and non-constant ratios, we can conclude that the sequence is an arithmetic sequence and not a geometric sequence.

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