What will be the next term in the sequence (1, 2, 6, 24, 120, …)?
Answer and explanation
Correct answer: 720
The governing concept is recognizing a multiplicative sequence generated by factorials. Each term is multiplied by the next positive integer: 1 × 2 = 2, 2 × 3 = 6, 6 × 4 = 24, and 24 × 5 = 120. The next operation must therefore multiply 120 by 6, giving 120 × 6 = 720. Equivalently, the displayed terms are 1!, 2!, 3!, 4!, and 5!, so the next term is 6! = 720. Hence option B is correct. Option A uses 5 instead of 6; 840 and 960 do not follow the successive-factor pattern. The sequence is not arithmetic or geometric because its differences and ratios are not constant.
Frequently asked questions
What is the correct answer to this question?
720
Why is this the correct answer?
The governing concept is recognizing a multiplicative sequence generated by factorials. Each term is multiplied by the next positive integer: 1 × 2 = 2, 2 × 3 = 6, 6 × 4 = 24, and 24 × 5 = 120. The next operation must therefore multiply 120 by 6, giving 120 × 6 = 720. Equivalently, the displayed terms are 1!, 2!, 3!, 4!, and 5!, so the next term is 6! = 720. Hence option B is correct. Option A uses 5 instead of 6; 840 and 960 do not follow the successive-factor pattern. The sequence is not arithmetic or geometric because its differences and ratios are not constant.
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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