Why is the sequence (2,6,12,20,\ldots) not a geometric progression?
Answer and explanation
Correct answer: Ratios of consecutive terms are not equal
In a geometric progression, the ratio of each term to the preceding term must remain constant. Here, \(6\div2=3\), but \(12\div6=2\) and \(20\div12=\frac{5}{3}\). Since these ratios differ, the sequence is not a geometric progression. Increasing terms or even terms do not make a sequence a GP. Exam tip: calculate ratios of consecutive terms and check whether they are equal.
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What is the correct answer to this question?
Ratios of consecutive terms are not equal
Why is this the correct answer?
In a geometric progression, the ratio of each term to the preceding term must remain constant. Here, \(6\div2=3\), but \(12\div6=2\) and \(20\div12=\frac{5}{3}\). Since these ratios differ, the sequence is not a geometric progression. Increasing terms or even terms do not make a sequence a GP. Exam tip: calculate ratios of consecutive terms and check whether they are equal.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Geometric Progression.
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