Question Detail
Question
Use principle of mathematical induction to find the value of k, where for all positive integers n, 2^(2n) + 3^(2n-2) is divisible by k.
Correct Answer
Option A is the correct answer.
Detailed Explanation
For n=1: 2² + 3⁰ = 4 + 1 = 5, divisible by 5. For n=2: 2⁴ + 3² = 16 + 9 = 25, divisible by 5. For n=3: 2⁶ + 3⁴ = 64 + 81 = 145, 145/5 = 29. It appears divisible by 5. This can be proven by induction.
Hint
Test with small values of n to find the common divisor.