Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPRINCIPLE OF MATHEMATICAL INDUCTION1 Mark
MCQ
For any natural number n, $7^n-2^n$ is divisible by
A
3
B
4
✓
5
D
7
✓
Answer
Correct option: C.
5
5
Solution:
Given, $7^n-2^n$
Let $\mathrm{n}=1$
$7^n-2^n=7^1-2^1=7-2=5$
which is divisible by 5
Let $\mathrm{n}=2$
$7^n-2^n=72-22=49-4=45$
which is divisible by 5
Let $\mathrm{n}=3$
$7^n-2^n=7^3-2^3=343-8=335$
which is divisible by 5
Hence, for any natural number $n, 7^n-2^n$ is divisible by 5
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