If a geometric progression has \(a_1=5\) and \(r=4\) what is \(a_3\)?
Answer and explanation
Correct answer: 80
The \(n\)th term of a geometric progression is \(a_n=a_1r^{n-1}\). Hence, \(a_3=5\times4^{3-1}=5\times16=80\). Therefore, 80 is correct. The close distractor 20 is the second term, \(a_2=5\times4\), not the third term. Exam tip: when finding the \(n\)th term, use \(n-1\) as the exponent of \(r\).
Frequently asked questions
What is the correct answer to this question?
80
Why is this the correct answer?
The \(n\)th term of a geometric progression is \(a_n=a_1r^{n-1}\). Hence, \(a_3=5\times4^{3-1}=5\times16=80\). Therefore, 80 is correct. The close distractor 20 is the second term, \(a_2=5\times4\), not the third term. Exam tip: when finding the \(n\)th term, use \(n-1\) as the exponent of \(r\).
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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