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If $a_{1} = 1 and a_{n} = {na}_{n - 1}$ for all positive integer $n \geq 2,$ then $a_{5}$ is equal to

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125

120

240

answer is B.

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Detailed Solution

Given, $a_{n} = n a_{n - 1}$

For $n = 2$

$a_{2} = 2 a_{1} = 2 (∵ a_{1} = 1 given)$

$a_{3} = 3 a_{2} = 3 (2) = 6$

$a_{4} = 4 (a_{3}) = 4 (6) = 24$

$a_{5} = 5 (a_{4}) = 5 (24) = 120$

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