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

are you able to find f(2) ?

Answer 2

i dont understand how to figure this question out at all i need alot of help

Answer 3

You start with f(n) = -3•f(n -1) - 2•f(n - 2)

Answer 4

and you replace every n with 2 to get

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

Answer 5

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

turns into

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

do you see what to do from here?

Answer 6

is it f(2)= 44!!!! :)

Answer 7

@jim_thompson5910

Answer 8

@jim_thompson5910 ?

Answer 9

incorrect

Answer 10

here's what you should get for f(2)


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

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

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

f(2) = -3*12 - 2*(-4)

f(2) = -36 + 8

f(2) = -28

Answer 11

my guess is that you somehow got 36+8 = 44

but keep in mind that 36 is negative

Answer 12

okay so now i know its -28 but there are two choices that have it so how can i figure out which of the two it is

Answer 13

@jim_thompson5910

Answer 14

f(0) = -4

that's the first term

Answer 15

basically -4 is the first term

Answer 16

f(1) = 12

so 12 is the second term

Answer 17

we just found that f(2) = -28

so the third term is -28

Answer 18

let's find f(3)


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

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

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

f(3) = -3*(-28) - 2*12

f(3) = 84 - 24

f(3) = 60

Answer 19

therefore, the fourth term is 60

Answer 20

oh my gosh thank you so much for the help i have some more questions like this and if you can help ill open up a new one @jim_thompson5910

Answer 21

sure I can help with a few more

Answer 22

thanks!!