What is the general term of the sequence (0,12,72,240,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^4-n^2\)
For \(a_n=n^4-n^2\), we get \(a_1=1-1=0\), \(a_2=16-4=12\), \(a_3=81-9=72\), and \(a_4=256-16=240\). Hence, the correct general term is \(a_n=n^4-n^2\). The close distractor \(2n^4\) gives \(a_1=2\), which does not match the first term 0. Exam tip: substitute \(n=1,2,3\) to verify a proposed general term against the initial terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^4-n^2\)
Why is this the correct answer?
For \(a_n=n^4-n^2\), we get \(a_1=1-1=0\), \(a_2=16-4=12\), \(a_3=81-9=72\), and \(a_4=256-16=240\). Hence, the correct general term is \(a_n=n^4-n^2\). The close distractor \(2n^4\) gives \(a_1=2\), which does not match the first term 0. Exam tip: substitute \(n=1,2,3\) to verify a proposed general term against the initial 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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