CBSE 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.
$5$
Given, $7^n– 2^n$
Let $n = 1$
$7^n-2^n$
$=7^1-2^1$
$=7-2$
$=5$
which is divisible by $5$
Let $n = 2$
$7^n-2^n$
$=7^2-2^2$
$=49-4$
$=45$
which is divisible by $5$
Let $n = 3$
$7^n-2^n$
$=7^3-2^3$
$=343-8$
$=335$
which is divisible by $5$
Hence, for any natural number $n, 7^n-2^n$ is divisible by $5$
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