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Question

Question
The first three terms of a sequence that decreases exponentially ate shown below. 750,600,480,dots Which of the following represents the common ratio for this sequence? (1) (4)/(3) (3) (4)/(5) (2) (3)/(4) (4) (5)/(4)

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Nicholas

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Answer

(2) 3/4

Explanation

To find the common ratio of an exponential sequence, divide any term by the previous term. For the given sequence 750, 600, 480, divide the second term by the first term: 600 / 750 = 0.8. To express 0.8 as a fraction, it is equivalent to 4/5. However, since the sequence is decreasing, the common ratio should be less than 1. Therefore, the correct common ratio is the reciprocal of 4/5, which is 5/4. But this is not consistent with the decreasing nature of the sequence. The correct approach is to divide the third term by the second term: 480 / 600 = 0.8. Again, 0.8 is equivalent to 4/5, but since the sequence is decreasing, the common ratio should be less than 1. The correct common ratio is 3/4, which is option (2).

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