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In the sequence (2,9,28,65,\ldots), the terms are of the form (n^3+1). What will be the next term?
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Answer and explanation
Correct answer: 126
The terms are \(1^3+1=2\), \(2^3+1=9\), \(3^3+1=28\), and \(4^3+1=65\). Therefore, the next term is \(5^3+1=125+1=126\). Although 128 is close, it equals \(5^3+3\), not the stated rule. Exam tip: verify a sequence rule by substituting \(n=1,2,3\) into it.
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What is the correct answer to this question?
126
Why is this the correct answer?
The terms are \(1^3+1=2\), \(2^3+1=9\), \(3^3+1=28\), and \(4^3+1=65\). Therefore, the next term is \(5^3+1=125+1=126\). Although 128 is close, it equals \(5^3+3\), not the stated rule. Exam tip: verify a sequence rule by substituting \(n=1,2,3\) into it.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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