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If a geometric progression has (a_3=45) and (r=3), what is (a_1)?
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Answer and explanation
Correct answer: 5
In a geometric progression, the third term is \(a_3=a_1r^2\). Thus, \(45=a_1\times 3^2=9a_1\), so \(a_1=45/9=5\). Option 15 is the second term \(a_2\), since \(5\times3=15\). Exam tip: use \(a_n=a_1r^{n-1}\) for the nth term of a GP.
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What is the correct answer to this question?
5
Why is this the correct answer?
In a geometric progression, the third term is \(a_3=a_1r^2\). Thus, \(45=a_1\times 3^2=9a_1\), so \(a_1=45/9=5\). Option 15 is the second term \(a_2\), since \(5\times3=15\). Exam tip: use \(a_n=a_1r^{n-1}\) for the nth term of a GP.
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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