Question

The following function defines a recursive sequence.

f(0) = -5

f(1) = 20

f(n) = -4•f(n -1) - 3•f(n - 2); for n > 1

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

-5, -20, -65, -200, …

-5, 20, -92, 372, …

-5, -24, -92, -372, …

-5, 20, -65, 200, …

Answer 1

what is the first term?

Answer 2

f(0) = -5 ?

Answer 3

yes, so they give you the first one

what is the second term?

Answer 4

we can narrow the options by eliminating the ones that have the wrong first and second terms, then the third term gets us to only one option that fits

Answer 5

we can use the rule given to determine f(2)

f(n) = -4•f(n -1) - 3•f(n - 2)

f(2) = -4•f(2 -1) - 3•f(2 - 2)

f(2) = -4•f(1) - 3•f(0)
^^ ^^
we already know these values
to plug into the rule

Answer 6

ok so what now ?

Answer 7

that IS the "what now" you work it out

Answer 8

or you ask questions about what it is you dont understand

Answer 9

oh ok hold on

Answer 10

i dont get what im suppose to work out ....

Answer 11

f(n) = -4•f(n -1) - 3•f(n - 2)

f(2) = -4•f(2 -1) - 3•f(2 - 2)

f(2) = -4•f(1) - 3•f(0)
^^ ^^
we already know these values
to plug into the rule

Answer 12

f(0) = -5

f(1) = 20

Answer 13

wherever you see f(0), replace it by -5

wherever you see f(1), replace it by 20

Answer 14

what if i see f(2)

Answer 15

f(2) is what we are calculating ... f(2) will equal ______________

Answer 16

f(2) = -4•f(1) - 3•f(0)
=-65 correct?

Answer 17

very good :)

Answer 18

so what we are looking for is a sequence that starts out:

f(0), f(1), f(2)

-5, 20, -65

only one of the options starts out like this

Answer 19

the last one ..

Answer 20

correct

Answer 21

thank you very much for explaining

Answer 22

good luck :)