Which general term is correct for the sequence (0,7,26,63,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^3-1\)
Taking the term number from \(n=1\), the rule \(a_n=n^3-1\) gives \(1^3-1=0\), \(2^3-1=7\), \(3^3-1=26\), and \(4^3-1=63\). Hence, option B is correct. The close distractor \(n^2-1\) gives \(3\) as its second term, not \(7\). Exam tip: substitute at least the first three values of \(n\) to verify a general term.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^3-1\)
Why is this the correct answer?
Taking the term number from \(n=1\), the rule \(a_n=n^3-1\) gives \(1^3-1=0\), \(2^3-1=7\), \(3^3-1=26\), and \(4^3-1=63\). Hence, option B is correct. The close distractor \(n^2-1\) gives \(3\) as its second term, not \(7\). Exam tip: substitute at least the first three values of \(n\) to verify a 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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