Question

WILL FAN AND MEDAL!!!!

Find f(5) for this sequence:

f(1) = 2 and f(2) = 5, f(n) = f(1) + f(2) + f(n - 1), for n > 2.

f(5) = ______

Answer 1

do you know what the notation " f(n) = f(1) + f(2) + f(n - 1)" means ?

Answer 2

no sadly... :( ive been studying on the lesson for this all day and i have yet to figure it out

Answer 3

we have

f(1) = 2 and f(2) = 5

and that's given to us

Answer 4

now let's say we want to find f(3)

Answer 5

for f(3), that's basically f(n) when n = 3

agreed?

Answer 6

ok hold on a sec i gots to read it first.... lol

Answer 7

ok yea agreed

Answer 8

so what we do is replace every copy of n with 3

Answer 9

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

f(3) = f(1) + f(2) + f(3 - 1)

f(3) = f(1) + f(2) + f(2)

Answer 10

what's next?

Answer 11

hold on i had to change my shirt cuz im gettin cold so yea...

Answer 12

um... you add the f(1)+f(2)+f(2)?

Answer 13

before you add, why not replace f(1) and f(2) with what they are equal to?

Answer 14

f(1) = 2
f(2) = 5

Answer 15

m my question is that how are u figuring out how to get what they are equal to...

Answer 16

that information of

f(1) = 2 and f(2) = 5

is given at the very top

Answer 17

so whoever wrote this problem just made it up and gave it to you

Answer 18

ooohhhh i see now ok so yea just a sec imma figure it out...

Answer 19

ok so f(3)=12?

Answer 20

correct

Answer 21

f(1) = 2
f(2) = 5
f(3) = 12

Answer 22

how do we find f(4) ?

Answer 23

idk im stuck....

Answer 24

hint:
\(\large {
f_1=2\qquad f_2=5\qquad f_{\color{brown}{ n}}=f_1+f_2+f_{\color{brown}{ n-1}}\qquad {\color{brown}{ n}}>2\\

\begin{array}{ccllll}
term\quad f(n)&value
\\\hline\\
1&2\\
2&5\\
{\color{brown}{ 3}}&f_1+f_2+f_{\color{brown}{ 3-1}}\\
&f_1+f_2+f_2\\
&2+5+5\\
4&f_1+f_2+f_{\color{brown}{ n-1}}\\
5&f_1+f_2+f_{\color{brown}{ n-1}}
\end{array}
}\)

Answer 25

replace every copy of n in f(n) = f(1) + f(2) + f(n - 1) with 4

Answer 26

ditto

Answer 27

and see what happens

Answer 28

\(\large {
\begin{array}{ccllll}
term\quad f(n)&value
\\\hline\\
1&2\\
2&5\\
{\color{brown}{ 3}}&f_1+f_2+f_{\color{brown}{ 3-1}}\\
&f_1+f_2+f_2\\
&2+5+5\\
{\color{brown}{ 4}}&f_1+f_2+f_{\color{brown}{ 4-1}}\\
{\color{brown}{ 5}}&f_1+f_2+f_{\color{brown}{ 5-1}}
\end{array} }\)

Answer 29

ok hold on.... does the f2 and all in the work is f(2)?

Answer 30

yeah \(\large f_{2}\) and f(2) are effectively the same thing just in different notation

Answer 31

ok just makin sure

Answer 32

f(2) is easier to write in plain text, so we'll stick with that

Answer 33

ok hold up a sec

Answer 34

f(4) = f(1) + f(2) + f(4 - 1)?
and then f(4) = 2 + 5 + 3 ?

Answer 35

f(4) = f(1) + f(2) + f(4 - 1)

f(4) = f(1) + f(2) + f(3)

f(4) = ???

Answer 36

notice how I wrote f(3) and not just 3 all by itself

Answer 37

so you can see how f(4) depends on f(3). You need to know the previous value of f(3) to get the value of f(4)

Answer 38

oohhhh ok yea i see now but i cant believe i have to do all this work for one freakin problem.... i miss when we had 5*10=whatever but getting off track yea i see how they depend on each other

Answer 39

it's not too bad once you get to know the problem better

Answer 40

oh and i have one question... do u do flvs and if so are u in 9th or 10th grade?

Answer 41

no I'm not in flvs

Answer 42

what are you getting for f(4) ?

Answer 43

f(4)=19?....

Answer 44

f(4) = f(1) + f(2) + f(4 - 1)

f(4) = f(1) + f(2) + f(3)

f(4) = 2 + 5 + 12

f(4) = 19

looks good

Answer 45

f(1) = 2
f(2) = 5
f(3) = 12
f(4) = 19

Answer 46

ok my other question is how in the world did u get two medals already when only one other person was in the problem for a sec? and yea

Answer 47

someone else gave it to me I think

Answer 48

oh

Answer 49

well i am goin to medal u right now cuz u are great at helpin people and there needs to be more people in life like u! :)

Answer 50

thanks

Answer 51

hopefully you see how to get f(5) ?

Answer 52

i do but just to make sure i need to do this f(n) = f(1) + f(2) + f(3) + f(4) + f(n-1) and replace the n with 5?

Answer 53

you always go back to the original equation they give you, which is f(n) = f(1) + f(2) + f(n - 1)

Answer 54

plug n = 5 into there

Answer 55

ok so
f(5) = f(1) + f(2) + f(3) + f(4) + f(5 - 1)?

Answer 56

no

Answer 57

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

f(5) = f(1) + f(2) + f(5 - 1)

Answer 58

I'm going back to the original equation they gave you

Answer 59

oh so i need to use the original equation to find all the f(1 through 5)?

Answer 60

well except for f(1) and f(2) because those are given to you

Answer 61

but yeah

Answer 62

ok yea so f(5)= f(1) + f(2) + f(5 - 1) ?

Answer 63

yes and you will keep going

Answer 64

well 5 is the number i need to find so yea

Answer 65

tell me what you get

Answer 66

ok hold on a sec

Answer 67

f(5)= f(1) + f(2) + f(5 - 1)

f(5)= f(1) + f(2) + f(4)

f(5)= 2 + 5 + 19

f(5)= 26?

Answer 68

you nailed it

Answer 69

:D !!

Answer 70

Thanks so much!!! imma fan u too cuz ur amazing thanks so much for helping me... u know... its hard to come by people like u.. thanks so much!! :D :) 11

Answer 71

you're welcome

Answer 72

thats suppose to be !! at the end lol

Answer 73

but yea thanks so much and i guess this is where we split paths so i will see u later my friend!

Answer 74

have a good day

Answer 75

u too! bye!