What is the general term of the sequence (2,16,54,128,\ldots)?
Answer and explanation
Correct answer: \(a_n=2n^3\)
Substituting \(n=1,2,3,4\) into \(2n^3\) gives \(2,16,54,128\), respectively. Hence, the general term is \(a_n=2n^3\). The closest distractor, \(2n^2\), gives the first term as 2, but for \(n=2\) it gives 8, not 16. Exam tip: verify a general term by checking it against at least the first three terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=2n^3\)
Why is this the correct answer?
Substituting \(n=1,2,3,4\) into \(2n^3\) gives \(2,16,54,128\), respectively. Hence, the general term is \(a_n=2n^3\). The closest distractor, \(2n^2\), gives the first term as 2, but for \(n=2\) it gives 8, not 16. Exam tip: verify a general term by checking it against at least the first three terms.
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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