If a geometric progression has \(a=7\) and \(r=2\), what is the fifth term?
Answer and explanation
Correct answer: 112
The \(n\)th term of a geometric progression is \(a_n=ar^{n-1}\). Therefore, \(a_5=7\times2^{5-1}=7\times16=112\). Hence, 112 is correct. The value 56 may result from incorrectly using \(2^3\). Exam tip: in the \(n\)th-term formula, the exponent of \(r\) is always \(n-1\).
Frequently asked questions
What is the correct answer to this question?
112
Why is this the correct answer?
The \(n\)th term of a geometric progression is \(a_n=ar^{n-1}\). Therefore, \(a_5=7\times2^{5-1}=7\times16=112\). Hence, 112 is correct. The value 56 may result from incorrectly using \(2^3\). Exam tip: in the \(n\)th-term formula, the exponent of \(r\) is always \(n-1\).
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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