Manuel bagged the plastic bottles after a recycling drive. He placed 121 bottles in the first bag, 144 bottles in the second bag, 169 bottles in the third bag, and 196 bottles in the fourth bag. What kind of sequence is this? Choices: (A)arithmetic (B)geometric (C)both (D)neither

Question

Manuel bagged the plastic bottles after a recycling drive. He placed 121 bottles in the first bag, 144 bottles in the second bag, 169 bottles in the third bag, and 196 bottles in the fourth bag. What kind of sequence is this?     Choices: (A)arithmetic (B)geometric (C)both (D)neither

Bytelearn · Accepted Answer

Identify Number of Bottles: First, let's list the number of bottles in each bag to see if we can identify a pattern: First bag: 121 bottles Second bag: 144 bottles Third bag: 169 bottles Fourth bag: 196 bottlesCheck for Arithmetic Sequence: To determine if this is an arithmetic sequence, we need to check if the difference between consecutive terms is constant. Difference between second and first bag: 144 - 121 = 23 Difference between third and second bag: 169 - 144 = 25 Difference between fourth and third bag: 196 - 169 = 27 Since the differences are not constant, this is not an arithmetic sequence.Check for Geometric Sequence: To determine if this is a geometric sequence, we need to check if the ratio between consecutive terms is constant. Ratio of second to first bag: 144 / 121 Ratio of third to second bag: 169 / 144 Ratio of fourth to third bag: 196 / 169 We can see that the ratios are not the same, so this is not a geometric sequence.Identify Perfect Squares Sequence: Since the sequence is neither arithmetic (constant difference) nor geometric (constant ratio), we need to consider other types of sequences. By examining the numbers, we notice that each number is a perfect square: 121 = 11^2 144 = 12^2 169 = 13^2 196 = 14^2 This sequence is a series of consecutive perfect squares.

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