If \(a=2\) and \(r=6\), what is \(a_4\)?
Answer and explanation
Correct answer: 432
The nth term of a geometric progression is \(a_n=ar^{n-1}\). Thus, \(a_4=2\times6^{4-1}=2\times6^3=2\times216=432\). Therefore, 432 is the correct option. \(216\) is only the value of \(6^3\); it still needs to be multiplied by the first term, \(a=2\). Exam tip: for the nth term, the exponent of \(r\) is \(n-1\), not \(n\).
Frequently asked questions
What is the correct answer to this question?
432
Why is this the correct answer?
The nth term of a geometric progression is \(a_n=ar^{n-1}\). Thus, \(a_4=2\times6^{4-1}=2\times6^3=2\times216=432\). Therefore, 432 is the correct option. \(216\) is only the value of \(6^3\); it still needs to be multiplied by the first term, \(a=2\). Exam tip: for the nth term, the exponent of \(r\) is \(n-1\), not \(n\).
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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