What is the general term of the sequence (9,27,81,243,\ldots)?
Answer and explanation
Correct answer: \(a_n=3^{n+1}\)
This is a geometric sequence because each term is 3 times the preceding term. For \(n=1\), the first term must be \(9=3^2\). Hence the exponent is \(n+1\), so \(a_n=3^{n+1}\). The rule \(a_n=3^n\) gives 3 as the first term, not 9. Exam tip: always substitute \(n=1\) to check a proposed general term.
Frequently asked questions
What is the correct answer to this question?
\(a_n=3^{n+1}\)
Why is this the correct answer?
This is a geometric sequence because each term is 3 times the preceding term. For \(n=1\), the first term must be \(9=3^2\). Hence the exponent is \(n+1\), so \(a_n=3^{n+1}\). The rule \(a_n=3^n\) gives 3 as the first term, not 9. Exam tip: always substitute \(n=1\) to check a proposed general term.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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