Question Detail
Question
If n ∈ Z⁺, then 5(5ⁿ) - 4n - 5 is divisible by
Correct Answer
Option C is the correct answer.
Detailed Explanation
For n=1: 5(5¹) - 4(1) - 5 = 25 - 4 - 5 = 16, divisible by 4? 16/4=4, but also by 8? Not divisible by 5,7,10. For n=2: 5(25) - 8 - 5 = 125 - 13 = 112, divisible by 7? 112/7=16, also divisible by 4. For n=3: 5(125) - 12 - 5 = 625 - 17 = 608, 608/4=152, 608/7 not integer. So it's divisible by 4 consistently.
Hint
Test with small values of n to find a pattern.