Question

The following function defines a recursive sequence.

f(0) = -4

f(1) = 12

f(n) = -3•f(n -1) - 2•f(n - 2); for n > 1

Which of the following sequences is defined by this recursive function?

-4, 12, -28, 60, …

-4, -12, -28, -60, …

-4, 12, -18, 54, …

-4, 12, -18, -54, …

Answer 1

@phi

Answer 2

this part
f(0) = -4

f(1) = 12

tells you the first 2 numbers. That lets you eliminate some of the choices.

Answer 3

This
f(n) = -3•f(n -1) - 2•f(n - 2); for n > 1

is a "rule" for figuring out the rest of the numbers
you know f(0) ( it is -4) and f(1) (it is 12) , the next number will be f(2)
(notice we want f(0), f(1), f(2), f(3), f(4), ... and so on)

to use the rule match f(n) with f(2)
the f's match, the parens match. you are supposed to notice that n matches with 2

that means in the rule, replace n with 2:
f(n) = -3•f(n -1) - 2•f(n - 2); for n > 1
Replace n with 2:
f(2) = -3*f(2-1) - 2*f(2-2)

now simplify: what is 2-1 ? it is 1
what is 2 - 2 ? it is 0

f(2) = -3*f(1) - 2*f(0)

next step: replace f(1) with its value (see above)
replace f(0) with its value
do the arithmetic and simplify to find f(2)