Question

Algebra 2 help please. Really confused

Answer 1

Consider this function in recursive form
f(1) = -2
f(n)= 4f(n-1) where n >
select the equivalent function for n >1

Answer 2

A) f(n) = -2n
B) f(n) = -2(n-1)
C) f(n) = 2(4)^n-1
D) f(n) = -2(n)^4

Answer 3

\[f(1)=-2\\
f(2)=4f(1)=4\times (-2)\]

Answer 4

\[f(3)=4\times f(2)=4\times 4\times (-2)=-2\times 4^2\]

Answer 5

\[f(4)=4\times f(3)=-2\times 4^3\]

Answer 6

and so on

Answer 7

I still don't quite get it. I literally have no idea what the question is asking or how to do it.

Answer 8

`f(1) = -2` means the first term of the sequence is -2

Do you agree with this statement @mach_15 ?

Answer 9

yeah

Answer 10

`f(n)= 4*f(n-1)` is the recursive rule

it helps you determine the second term, third term, etc

to find the second term, plug in n = 2

f(n)= 4*f(n-1)
f(2)= 4*f(2-1) ... replace every 'n' with '2'
f(2)= 4*f(1)
f(2) = 4*(-2) ... replace f(1) with -2
f(2) = -8

So the second term is -8. Notice how i used the first term (f(1) = -2) to find the second term

Answer 11

let me know if that makes sense or not

Answer 12

Yes it does

Answer 13

what is f(3) equal to?

Answer 14

I don't think I did this right at all but I got 8.

Answer 15

we'll use the fact that f(2) = -8


let's plug in n = 3

f(n) = 4*f(n-1)
f(3) = 4*f(3-1) ... replace every 'n' with '3'
f(3) = 4*f(2)
f(3) = 4*(-8) ... replace f(2) with -8 (see above)
f(3) = -32


make sense?

Answer 16

if you want to find the fourth term, use the fact that the third term is f(3) = -32

Answer 17

oh okay I see now. so the fourth term is -128?

Answer 18

f(n) = 4*f(n-1)
f(4) = 4*f(4-1) ... replace every 'n' with '4'
f(4) = 4*f(3)
f(4) = 4*(-32) ... replace f(3) with -32 (see above)
f(4) = -128

yep you got it

Answer 19

so the sequence of terms is
-2, -8, -32, -128, ...
and it goes on forever

Answer 20

The question is: which function in your list of choices also produces that same exact sequence?

Answer 21

Let's test choice `A) f(n) = -2n`


first term happens when n = 1
f(n) = -2n
f(1) = -2*1 ... plug in n = 1
f(1) = -2
first term is -2. So far so good


second term happens when n = 2
f(n) = -2n
f(2) = -2*2 ... plug in n = 2
f(2) = -4
uh oh. We got -4 to be the second term when it should be -8. So choice A can't be the answer because the sequences don't match up

Recall that we want -2, -8, -32, -128, ... to be our sequence where n starts at n = 1.

Answer 22

Oh okay. So I guess ill try B and see if I do it right

Answer 23

ok tell me what you get

Answer 24

I got 0. Did I do it right?

Answer 25

I went ahead and did C and D and C = 2 but D = -2 so the answer would be D right?

Answer 26

B) f(n) = -2(n-1)

first term
n = 1
f(n) = -2*(n-1)
f(1) = -2*(1-1)
f(1) = 0

yep so because the first term (0) doesn't match with the first term we want (-2) this means choice B is out

Answer 27

D) f(n) = -2(n)^4

let's find the second term using the function in choice D

plug in n = 2
f(n) = -2(n)^4
f(2) = -2(2)^4
f(2) = -2*(16)
f(2) = -32

we don't have a match. We wanted the second term to be -8 and not -32

So choice D is out

Answer 28

I'm thinking there's a typo. I think your teacher meant to write -2(4)^(n-1) for choice C

Answer 29

Maybe. Its an online multiple choice quiz through K12 so I don't know.

Answer 30

Thank you for all your help! This stuff makes a lot more sense now!

Answer 31

I'm glad it does