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Paper 1 · November 2010 · Series and Proof by Induction

Find the value of $10^n + 12\left(4^{n+1}\right) + 5$ when $n = 1$ .

Model answer

207

Explanation

10^1=10

and

4^{1+1}=16

, so

12\times16=192

. The total is

10+192+5=207

. Since

207=9\times23

, the expression is divisible by 9 when

n=1

, which settles the basis of the induction.

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

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