Which is the correct rule for the sequence (0,3,8,15,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^2-1\)
Taking the term number as \(n=1,2,3,4,\ldots\), the rule \(a_n=n^2-1\) gives \(1^2-1=0\), \(2^2-1=3\), \(3^2-1=8\), and \(4^2-1=15\). Hence, option B is correct. Option C gives \(0,2,4,6,\ldots\), which is a linear pattern and does not match the given sequence. Exam tip: substitute \(n=1,2,3,4\) to verify an explicit rule quickly.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2-1\)
Why is this the correct answer?
Taking the term number as \(n=1,2,3,4,\ldots\), the rule \(a_n=n^2-1\) gives \(1^2-1=0\), \(2^2-1=3\), \(3^2-1=8\), and \(4^2-1=15\). Hence, option B is correct. Option C gives \(0,2,4,6,\ldots\), which is a linear pattern and does not match the given sequence. Exam tip: substitute \(n=1,2,3,4\) to verify an explicit rule quickly.
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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