Solution: 2014 Winter Final - 10

Author: Michiel Smid

Question

Consider the following recursive function:

$f(0)$	$\;=\;$	$3,$
$f(n + 1)$	$\;=\;$	$f(n) + 10n + 2\; \ \text{for all}$ $\text{integers}\ n \geq 0.$

Which of the following is true?

(a)

for all $n \geq 0$: $f(n) = 5n^{2} - 3n + 3$

(b)

for all $n \geq 0$: $f(n) = 5n^{2} - 2n + 3$

(c)

for all $n \geq 0$: $f(n) = 5n^{2} + 3n + 3$

(d)

for all $n \geq 0$: $f(n) = 5n^{2} - 3n + 2$

Calculate $ f(1) $ $ f(1) = f(0) + 10(0) + 2 $

$ f(1) = 3 + 0 + 2 $

$ f(1) = 5 $

Now, we test