Question

The following function defines a recursive sequence.

f(0) = -3

f(1) = 6

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

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

-3, 6, -9, -12, …

-3, 20, -95, 480, …

-3, 6, -9, 12, …

-3, -20, -95, -480, …

Answer 1

I have never been thought this for some reason I am looking for someone to tell me how to do it.

Answer 2

taught*

Answer 3

ok,
f(0) = -3 , first term = -3

f(1) = 6, 2nd term = 6
so, as of now our sequence is -3,6

to find nect term, we will use
f(n) = -2•f(n -1) - f(n - 2)

put n= 2 here, what do u get ?

Answer 4

Im sorry, but I lost you at f(n) = -2•f(n -1) - f(n - 2)

Answer 5

thats what is already given.

you just replace "n" by "2" there,
to get f(2)

Answer 6

Oh ok

Answer 7

So it would be like f(2) = -2 * f(n-1) - f(n - 2) to keep going correct?

Answer 8

you need to replace n by 2 on right side too!

Answer 9

Oh so.. f(2) = -2 * f(2 - 1) - f(2 - 2)?

Answer 10

yes!
f(2) = -2 f(1) - f(0)

and you already know
f(1) =6, f(0) = -3
just plug in values!

Answer 11

Oh ok so the answer would be the first one right?

Answer 12

you need to find f(3) too!
f(3) = - 2f(2) - f(1) = - 2(-9) -6 = 18-6 = 12

Answer 13

so no, its not the first one

Answer 14

Oh ok since 18 - 6 is positive 12 not negative. I messed up on that last part I thought it was 6- 18. Thank you I understand now!

Answer 15

welcome ^_^