What is the general term of the sequence (7,25,61,121,\ldots)?
Answer and explanation
Correct answer: \(a_n=(n+1)^3-n\)
Substituting \(n=1,2,3,4\) into \(a_n=(n+1)^3-n\) gives \(7,25,61,121\), respectively. Therefore, option A is correct. Option B gives the first term as \(7\), but for \(n=2\) it gives \(14\), not \(25\). Exam tip: verify a proposed general term using at least the first three terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=(n+1)^3-n\)
Why is this the correct answer?
Substituting \(n=1,2,3,4\) into \(a_n=(n+1)^3-n\) gives \(7,25,61,121\), respectively. Therefore, option A is correct. Option B gives the first term as \(7\), but for \(n=2\) it gives \(14\), not \(25\). Exam tip: verify a proposed general term using 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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