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Principle of Mathematical Induction — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsPrinciple of Mathematical Induction1 Mark
MCQ
For all $n \in N, 3^{2n} + 7$ is divisible by:
  • ✓
    $8$
  • B
    $3$
  • C
    $11$
  • D
    non of these
✓

Answer

Correct option: A.
$8$
Given number $= 32n + 7$
Let $n = 1, 2, 3, 4, ……..$
$3^{2 n}+7=3^2+7=9+7=16$
$3^{2 n}+7=3^4+7=81+7=88$
$3^{2 n}+7=3^6+7=729+7=736$
Since, all these numbers are divisible by $8$ for $n = 1, 2, 3, …..$
So, the given number is divisible by $8$

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