What are (a) and (r) in the geometric progression (3,18,108,648,\ldots)?
Answer and explanation
Correct answer: \(a=3,\ r=6\)
In a geometric progression, the first term is \(a\), so \(a=3\). The common ratio \(r\) is found by dividing a term by the preceding term: \(r=\frac{18}{3}=6\). Checking, \(18\times6=108\) and \(108\times6=648\). Hence, \(a=3,\ r=6\). In option D, the ratio is correct, but 18 is not the first term. Exam tip: identify the first term as \(a\), then divide consecutive terms to find \(r\).
Frequently asked questions
What is the correct answer to this question?
\(a=3,\ r=6\)
Why is this the correct answer?
In a geometric progression, the first term is \(a\), so \(a=3\). The common ratio \(r\) is found by dividing a term by the preceding term: \(r=\frac{18}{3}=6\). Checking, \(18\times6=108\) and \(108\times6=648\). Hence, \(a=3,\ r=6\). In option D, the ratio is correct, but 18 is not the first term. Exam tip: identify the first term as \(a\), then divide consecutive terms to find \(r\).
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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