While organizing her DVD collection, Janet put 21 DVDs on the first rack, 29 DVDs on the second rack, 37 DVDs on the third rack, and 45 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, Janet put 21 DVDs on the first rack, 29 DVDs on the second rack, 37 DVDs on the third rack, and 45 DVDs on the fourth rack. What kind of sequence is this?     Choices: (A)arithmetic (B)geometric (C)both (D)neither

Bytelearn · Accepted Answer

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 racks: Difference between the second rack and the first rack: 29 - 21 = 8 Difference between the third rack and the second rack: 37 - 29 = 8 Difference between the fourth rack and the third rack: 45 - 37 = 8Confirm Arithmetic Sequence: Since the differences between consecutive terms are constant, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a constant difference between consecutive terms.Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms: Ratio of the second rack to the first rack: 29 / 21 Ratio of the third rack to the second rack: 37 / 29 Ratio of the fourth rack to the third rack: 45 / 37Calculate Ratios: We calculate the ratios: 29 / 21 ≈ 1.38 37 / 29 ≈ 1.28 45 / 37 ≈ 1.22 Since the ratios are not constant, the sequence is not geometric. A geometric sequence is defined by having a constant ratio between consecutive terms.

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