In the sequence (2,4,12,48,240,\ldots), the multiplier pattern is (2,3,4,5,\ldots). What will be the next term?
Answer and explanation
Correct answer: 1440
The successive terms are multiplied by 2, 3, 4, and 5: \(2\times2=4\), \(4\times3=12\), \(12\times4=48\), and \(48\times5=240\). Therefore, the next multiplier is 6, so the next term is \(240\times6=1440\). Option 1200 would repeat multiplication by 5, which does not follow the increasing multiplier pattern. Exam tip: divide consecutive terms to identify a changing-multiplier pattern.
Frequently asked questions
What is the correct answer to this question?
1440
Why is this the correct answer?
The successive terms are multiplied by 2, 3, 4, and 5: \(2\times2=4\), \(4\times3=12\), \(12\times4=48\), and \(48\times5=240\). Therefore, the next multiplier is 6, so the next term is \(240\times6=1440\). Option 1200 would repeat multiplication by 5, which does not follow the increasing multiplier pattern. Exam tip: divide consecutive terms to identify a changing-multiplier pattern.
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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