alleryStart learning →Is the sequence 48, 12, 4, 2 geometric?
AYes, with a common ratio of 1/4
BYes, with a common ratio of 1/3
CNo, the ratios are not all equal
DNo, the terms are not all integers
Answer & Solution
Correct answer: C. No, the ratios are not all equal
1. Divide the second term by the first: 12/48 = 1/4.
2. Divide the third by the second: 4/12 = 1/3.
3. Divide the fourth by the third: 2/4 = 1/2.
4. The quotients 1/4, 1/3 and 1/2 are not equal, so no common ratio exists and the sequence is not geometric.
5. Reading only the first quotient would suggest a ratio of 1/4, which is why the check must be repeated across the sequence.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.3 Geometric Sequences_
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