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PRINCIPLE OF MATHEMATICAL INDUCTION — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPRINCIPLE OF MATHEMATICAL INDUCTION1 Mark
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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