What is the general term of the geometric progression (3,9,27,81,\ldots)?
Answer and explanation
Correct answer: \(a_n=3^n\)
Here, the first term is \(a=3\) and the common ratio is \(r=3\). Thus, \(a_n=ar^{n-1}=3\times3^{n-1}=3^n\). The option \(a_n=3^{n-1}\) gives 1 as the first term, not 3. Exam tip: substitute \(n=1\) to check whether a proposed general term gives the first term of the sequence.
Frequently asked questions
What is the correct answer to this question?
\(a_n=3^n\)
Why is this the correct answer?
Here, the first term is \(a=3\) and the common ratio is \(r=3\). Thus, \(a_n=ar^{n-1}=3\times3^{n-1}=3^n\). The option \(a_n=3^{n-1}\) gives 1 as the first term, not 3. Exam tip: substitute \(n=1\) to check whether a proposed general term gives the first term of the sequence.
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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