An induction proof shows that 10^n + 12(4^n+1) + 5 is divisible by 9 for every positive integer n. What does the inductive step assume?

An induction proof shows that $10^n + 12\left(4^{n+1}\right) + 5$ is divisible by 9 for every positive integer $n$ . What does the inductive step assume?

Athe result holds for every positive integer n

Bthe result holds for n = 1 and for n = 2

C9 is a factor of 10^k for that value of k

Dthe result holds for one value n = k

Explanation

Induction assumes the statement for a single unnamed value

n=k

, then uses that assumption to prove it for

n=k+1

. Assuming it for every

n

would be assuming the very thing to be proved.

Derived from ZIMSEC Further Mathematics 9187/1, November 2010, Q6

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