Gujarat 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
17
Solution:
$3.5^{2n+ 1} + 2^{3n+1}$ 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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