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Mathematical Induction — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSMathematical Induction1 Mark
MCQ
For all $\mathbf{n} \in \mathbf{N}, 3 \times 5^{2 n+1}+2^{3 n+1}$ is divisible by:
  • A
    19
  • ✓
    17
  • C
    23
  • D
    25
✓

Answer

Correct option: B.
17
  1. 17
Solution:
$3.5^{2 n+1}+2^{3 n+1}$ is divisible by $17, n \in N$
Step 1: $3.5^{2(1)+1}+2^{3(1)+1}$
$3.5^3+2^4=391$
Step 2: Assuming True for $\mathrm{n}=\mathrm{k}$
Hence, it is proved that $3.5^{2 n+1}+2^{3 n+1}$ is divisible by 17 .

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