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Principle of Mathematical Induction — Maths STD 11 Science — Question

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$
$= 72 – 22$
$= 49 – 4$
$= 45$
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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