Question

The following function defines a recursive sequence:
f(0) = -2
f(1) = 8
f(n) = -4•f(n -1) - 3•f(n - 2); for n > 1
Which of the following sequences is defined by this recursive function?
-2,8,-26,-80, …
-2,8,-26,80, …
-2,12,-44,180,…
-2,-12,-44,-180, …

Answer 1

well the first two terms are already given
-2,8,...
we can find the third term by replacing n with 2

Answer 2

\[f(n)=-4f(n-1)-3f(n-2) \\ f(2)=-4f(2-1)-3f(2-2) \\ f(2)=-4f(1)-3f(0)\]
now plug in the values you were given for f(0) and f(1)
and apply order of operations to find f(2)

Answer 3

i am lost... lol

Answer 4

do you know what f(1) and f(0) equal?

Answer 5

8, -2

Answer 6

well plug those in then

Answer 7

\[f(n)=-4f(n-1)-3f(n-2) \\ f(2)=-4f(2-1)-3f(2-2) \\ f(2)=-4f(1)-3f(0) \\ f(2)=-4(8)-3(-2)\]
do you know order of operations?

Answer 8

not really, can you explain it to me?

Answer 9

1) exponents
2) grouping symbols
3) mult/divide as it occurs left to right
4) add/subtract as it occurs left to right

Answer 10

you only have multiplication and subtraction
-4(8)=?
3(-2)=?
then subtract the bottom product from the top

Answer 11

-2 - (-32)
-2 + 32
30

Answer 12

3(-2) is -6

Answer 13

-4(8)=-32

Answer 14

-32-(-6)=?

Answer 15

-26

Answer 16

\[f(n)=-4f(n-1)-3f(n-2) \\ f(2)=-4f(2-1)-3f(2-2) \\ f(2)=-4f(1)-3f(0) \\ f(2)=-4(8)-3(-2) \\ f(2)=-32-(-6) \\ f(2)=-32+6 \\ f(2)=-26 \]

ok use \[f(n)=-4f(n-1)-3f(n-2) \]
again to find the 4th term in the sequence called f(3)
f(3)
so that means we want to replace n's with 3 now

Answer 17

f(3)=−4f(3−1)−3f(3−2)

Answer 18

right so far

Answer 19

and 3-1=2 and 3-2=1
so you have
f(3)=-4f(2)-3f(1)

Answer 20

you already know f(1) and you just found f(2)

Answer 21

f(3)=-4(-26)-3(8)

Answer 22

yep now just apply the order of operations

Answer 23

f(3)=-104-24?

Answer 24

almost
keep in mind a neg times a neg=pos

Answer 25

so f(3)=104-24

Answer 26

sorry my computer froze

Answer 27

f(3)=80

Answer 28

great
do you see your sequence

Answer 29

yes i do :) thanks for all your help freckles! greatly appreciate it :)

Answer 30

you had
f(0)=-2
f(1)=8
f(2)=-26
f(3)=80
so your sequence
should look like this
-2,8,-26,80,...


and great work! :)