What are (a) and (r) in the geometric progression (2,10,50,250,\ldots)?
Answer and explanation
Correct answer: \(a=2,\ r=5\)
In a geometric progression, \(a\) is the first term, so \(a=2\). The common ratio \(r\) is the quotient of consecutive terms: \(r=\frac{10}{2}=5\). This is confirmed by \(50\div10=5\) and \(250\div50=5\). In option D, the ratio is correct, but the first term is 2, not 10. Exam tip: identify \(a\) from the first term and find \(r\) by dividing the second term by the first.
Frequently asked questions
What is the correct answer to this question?
\(a=2,\ r=5\)
Why is this the correct answer?
In a geometric progression, \(a\) is the first term, so \(a=2\). The common ratio \(r\) is the quotient of consecutive terms: \(r=\frac{10}{2}=5\). This is confirmed by \(50\div10=5\) and \(250\div50=5\). In option D, the ratio is correct, but the first term is 2, not 10. Exam tip: identify \(a\) from the first term and find \(r\) by dividing the second term by the first.
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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