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Mathematical Induction — Maths STD 11 Science — Question

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

Answer

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

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