What is the general term of the sequence (2,6,22,74,\ldots)?
Answer and explanation
Correct answer: \(a_n=3^n-2n+1\)
Substituting \(n=1,2,3,4\) into \(a_n=3^n-2n+1\) gives \(2,6,22,74\), respectively. Hence, it is the general term. The close distractor \(2^n+n\) gives 3 as its first term, not 2. Exam tip: verify a proposed general term by checking it for at least the first three values of \(n\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=3^n-2n+1\)
Why is this the correct answer?
Substituting \(n=1,2,3,4\) into \(a_n=3^n-2n+1\) gives \(2,6,22,74\), respectively. Hence, it is the general term. The close distractor \(2^n+n\) gives 3 as its first term, not 2. Exam tip: verify a proposed general term by checking it for at least the first three values of \(n\).
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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