MCQ
For every positive integer $n, 7^n– 3^n$ is divisible by:
- A$3$
- ✓$4$
- C$7$
- D$5$
✓
Answer
Correct option: B.
$4$
Let $P(n) = 7^n- 3^n$
Substituting $n = 1, 2, 3,…$
$P(1) = 7^1– 3^1= 7 - 3 = 4 $
$P(2) = 7^2- 3^2= 49 - 9 = 40 $
$P(3) = 7^3-3^3= 343 - 27 = 316 $
Thus, for every positive integer $n, 7^n-3^n $ is divisible by $4.$
Substituting $n = 1, 2, 3,…$
$P(1) = 7^1– 3^1= 7 - 3 = 4 $
$P(2) = 7^2- 3^2= 49 - 9 = 40 $
$P(3) = 7^3-3^3= 343 - 27 = 316 $
Thus, for every positive integer $n, 7^n-3^n $ is divisible by $4.$
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