Question Detail
Question
If f(n) = 2ⁿ + 6ⁿ, then what is f(k+1)?
Correct Answer
Option A is the correct answer.
Detailed Explanation
f(k+1) = 2^(k+1) + 6^(k+1) = 2·2ᵏ + 6·6ᵏ. Now 6·6ᵏ = 6f(k) - 6·2ᵏ. So f(k+1) = 6f(k) - 6·2ᵏ + 2·2ᵏ = 6f(k) - 4·2ᵏ.
Hint
Write 6^(k+1) as 6·6ᵏ and relate to f(k).