CBSE BoardEnglish MediumSTD 11 ScienceMathsPrinciple of Mathematical 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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