Which general term is correct for the sequence (3,9,27,81,\ldots)?
Answer and explanation
Correct answer: \(a_n=3^n\)
This is a geometric sequence in which each term is 3 times the previous term. Starting with \(n=1\), we get \(a_1=3^1=3\), \(a_2=3^2=9\), \(a_3=3^3=27\), and \(a_4=3^4=81\). Hence, the correct general term is \(a_n=3^n\). The rule \(a_n=3n\) would give 3, 6, 9, 12, so it is not correct. Exam tip: Substitute \(n=1\) in a proposed rule to check the first term.
Frequently asked questions
What is the correct answer to this question?
\(a_n=3^n\)
Why is this the correct answer?
This is a geometric sequence in which each term is 3 times the previous term. Starting with \(n=1\), we get \(a_1=3^1=3\), \(a_2=3^2=9\), \(a_3=3^3=27\), and \(a_4=3^4=81\). Hence, the correct general term is \(a_n=3^n\). The rule \(a_n=3n\) would give 3, 6, 9, 12, so it is not correct. Exam tip: Substitute \(n=1\) in a proposed rule to check the first 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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