n(n + 1) (n + 5) is a multiple of: - Vidyadip

MCQ

$n(n + 1) (n + 5)$ is a multiple of:

✓
$3$
B
$8$
C
$5$
D
$7$

✓

Answer

Correct option: A.

$3$

Let $P(n) = n(n + 1)(n + 5)$
Substituting $n = 1, 2, 3,….$
$P(1) = 1(1 + 1)(1 + 5) = 2(6) = 12;$ multiple of $2, 3, 4, 6$
$P(2) = 2(2 + 1)(2 + 5) = 2(3)(7) = 42;$ multiple of $2, 3, 6, 7$
$P(3) = 3(3 + 1)(3 + 5) = 3(4)(8) = 96;$ multiple of $2, 3, 4, 6, 8, 12$

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