What are (a) and (r) in the geometric progression (1,5,25,125,\ldots)?
Answer and explanation
Correct answer: \(a=1,\ r=5\)
In a geometric progression, \(a\) is the first term, so \(a=1\). The common ratio \(r\) is obtained by dividing a term by the preceding term: \(r=\frac{5}{1}=5\). Therefore, \(a=1,\ r=5\) is correct. \(r=25\) is incorrect because it compares the first and third terms, not consecutive terms. Exam tip: find \(r\) by dividing the second term by the first term.
Frequently asked questions
What is the correct answer to this question?
\(a=1,\ r=5\)
Why is this the correct answer?
In a geometric progression, \(a\) is the first term, so \(a=1\). The common ratio \(r\) is obtained by dividing a term by the preceding term: \(r=\frac{5}{1}=5\). Therefore, \(a=1,\ r=5\) is correct. \(r=25\) is incorrect because it compares the first and third terms, not consecutive terms. Exam tip: find \(r\) by dividing the second term by the first term.
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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