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?

Answer 1

options
-4, 12, -28, 60, …

-4, -12, -28, -60, …

-4, 12, -18, 54, …

-4, 12, -18, -54, …

Answer 2

f(n-1) is the previous term
f(n-2) is the term before the previous term

Eg. to find the third term, you need the 2nd term, and the 1st term

Answer 3

the first two terms are -4, 12

Answer 4

right?

Answer 5

Yes. Use to find the next, using f(n) = -3•f(n -1) - 2•f(n - 2)

Answer 6

wait so how do you use the first two and apply it to that equaton?

Answer 7

@agent0smith

Answer 8

f(n) = -3•f(n -1) - 2•f(n - 2)

f(n-1) is the first term. f(n-2) is the 2nd. Plug them in.

Answer 9

ok so f(n)=-3 x -4 - 2 x 12 ?

Answer 10

Yes

Answer 11

and solve?

Answer 12

f(n) = -12 ?

Answer 13

You shouldn't really need to ask "and solve?"... you should probably be able to figure out whether you should solve it or not...

Yes and no, f(3) = -12, not f(n)

Answer 14

oh sorry im not that good with sequences

Answer 15

Now find the next term the same way.

f(n) = -3•f(n -1) - 2•f(n - 2)

Now to find f(4), you need to use f(3) and f(2), and plug them in.

Answer 16

where do I plug them in? which in which

Answer 17

f(2) inside f(n-1) and f(3) inside the other?

Answer 18

You're finding f(4), so n=4...

f(4) = -3•f(4 -1) - 2•f(4 - 2)

Answer 19

ohhhhhhh ok hold on let me solve that

Answer 20

f(4)=12

Answer 21

?

Answer 22

@agent0smith

Answer 23

why are they all the same

Answer 24

I think its a

Answer 25

Because you didn't actually plug in the numbers... also we were 1 ahead, we're finding f(3)

f(3) = -3•f(3 -1) - 2•f(3 - 2)

First simplify this. Do not skip straight to the answer like last time.

Answer 26

Oh you messed up finding the last term... find f(2) again.

f(2) = -3•f(2 -1) - 2•f(2 - 2)

First simplify the stuff in brackets.

Answer 27

oh boy this is complicated lol

Answer 28

f(2)=10

Answer 29

It's not, if you use what i said earlier...

Eg. to find the third term, you need the 2nd term, and the 1st term
to find the fourth term, you need the 3rd term and 2nd term

if you're finding f(3), you'd need f(2) and f(1).

First, find f(2), correctly:

f(n) = -3•f(n -1) - 2•f(n - 2)
^f(2) ^f(1) ^f(0)

Answer 30

yes that's what I did I guess im just not good at this lol

Answer 31

is the second term -12?

Answer 32

f(0) = -4, f(1) = 12

Find f(2) using those.

Answer 33

what?

Answer 34

im officially 100% confused

Answer 35

f(n) = -3•f(n -1) - 2•f(n - 2)
^f(2) ^f(1) ^f(0)


f(0) = -4,
f(1) = 12

Answer 36

ohhh ok so hold on let me get f(2)

Answer 37

-28

Answer 38

so its a! right?

Answer 39

Thank You!

Answer 40

It could be B, since...

-4, 12, -28, 60, …

-4, -12, -28, -60, …

But it is A.

Answer 41

thank you!