Question Detail
Question
If f(n) = 2^n + 6^n, 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) = 2·2^k + 6·6^k. We want to express in terms of f(k) = 2^k + 6^k. 6·6^k = 6·6^k, and 2·2^k = 2·2^k. To get 6·6^k, we can write 6·6^k = 6f(k) - 6·2^k. Then f(k+1) = 6f(k) - 6·2^k + 2·2^k = 6f(k) - 4·2^k.
Hint
Express f(k+1) in terms of f(k) by factoring.