Question

Medal to whoever helps. (Algebra 1)

Answer 1

what do you need help with

Answer 2

help

Answer 3

Algebra 1, duh.

Answer 4

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 5

answer: ☺

Answer 6

I can't see anything...

Answer 7

Try refresh page.

Answer 8

can you explain it to me? The problem...

Answer 9

please help.

Answer 10

So you are given that \(f(0) = -5\) and \(f(1)=20\). we need to find next few terms: \(f(2),~f(3),~\ldots\)

we are given equation \(f(n) = -4~f(n -1) - 3~f(n - 2)\)

So to find \(f(2)\), you have \(f(\color{red}{2}) = -4~f(\color{red}{2} -1) - 3~f(\color{red}{2} - 2)\\~~~~~~~=-4~f(1) - 3~f(0)\)

We are given that \(f(0) = -5\) and \(f(1)=20\), right?

So \(\cdots=-4 (20)-3(-5)=\cdots~?\)

Answer 11

Is that clear?

Answer 12

0.o

Answer 13

Doesn't sound good...

Answer 14

ok so \[n\] equals what ever number we need?

Answer 15

Right.

Answer 16

I'm starting to get it.

Answer 17

ok, so can you find third term: \(f(2)\)?

Answer 18

hang on...

Answer 19

\[f(2)=-4f(1)-34\] ?

Answer 20

that last bit was supposed to be 3f

Answer 21

\(f(2)=-4f(1)-3f(0)\)

Answer 22

alright. now what?

Answer 23

You just replace \(f(1)\) with \(20\) and \(f(0)\) with \(-5\)

So you have \(f(2)=-4[20]-3[-5]\)

Answer 24

so it should be b?

Answer 25

A or D to me?

You got -92?

Answer 26

-95

Answer 27

\(-4[20]=-80\) and \(-3[-5]=15\)

So \(f(2)=-80+15=\cdots~?\)

Answer 28

oh you add them?

Answer 29

wait that still doesn't work...

Answer 30

well, that's because you multiply negative number. Made it positive, so you add them.

Answer 31

it adds up to -65

Answer 32

Right, so that leave us A or D. Now find \(f(3)\).

From recursive formula, we have \(f(3) = -4f(2)-3f(1)\)

Replace \(f(2)\) with \(-65\) and \(f(1)\) with \(20\)

Answer 33

but earlier you said -92...

Answer 34

No? I just asked if you got -92?

f(2) is actually -65.

Answer 35

oh, so f(3) is 320?

Answer 36

No? You have \(f(3)=-4[-65]-3[20]\), right?

-4 times -65 is 260, right?
-3 times 20 is -60, right?

So you have \(f(3)=260-60=\cdots~?\)

Answer 37

I ended up with \[f(3)= 260+60\] because \[-3(20)\] is a negative right?

Answer 38

Yeah it is negative, so you are supposed to subtract 60 from 260

Answer 39

if you have two minus signs, they will cancel each other out, so you end up with positive.

But this time, you only have one minus sign. so that's subtraction.

Answer 40

but isn't that a double negative (sorry about my stupidity I'm awful at math)

Answer 41

You multiplied -3 by 20, which is -60.

20 is positive.

Answer 42

ok.

Answer 43

So does it make sense?

Answer 44

yes

Answer 45

so D.?

Answer 46

Ok, so your answer is D.

I didn't notice that 20 is negative in A, lol...

Answer 47

Thank you SOOOOO much!

Answer 48

No problem