Question

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

what is f(3)?

Answer 2

i think it 9 but I'm not sure

Answer 3

let's find out. f(3) happens when n = 3

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

f(3) = f(1) + f(2) + f(3 - 1) ... replace all copies of n with 3

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

f(3) = 2 + 5 + 5

f(3) = 12

Answer 4

see how I got 12?

Answer 5

yea so... whats next, thats where i get kind of lost

Answer 6

what is f(4)

Answer 7

10?

Answer 8

no

Answer 9

f(4) happens when n = 4

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

f(4) = f(1) + f(2) + f(4 - 1) ... replace all copies of n with 4

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

f(4) = ??

Answer 10

oh so its 22?

Answer 11

what is f(1)

Answer 12

2

Answer 13

what is f(2)

Answer 14

5

Answer 15

what is f(3)

Answer 16

12

Answer 17

f(4) happens when n = 4

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

f(4) = f(1) + f(2) + f(4 - 1) ... replace all copies of n with 4

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

f(4) = 2 + 5 + 12

f(4) = 19

Answer 18

ok so the f(5)=F(!)+f(2)+f(3)+f(4)

Answer 19

no you follow the definition f(n) = f(1) + f(2) + f(n - 1)

Answer 20

and plug in n = 5

Answer 21

so f(5)=11

Answer 22

no f(5) has to be bigger than f(4)

Answer 23

f(5) happens when n = 5

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

f(5) = f(1) + f(2) + f(5 - 1) ... replace all copies of n with 5

Answer 24

ok so it would look like this
f(5) = 2+ 5 + (5 - 1)

Answer 25

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

Answer 26

i see how you got 11 now

Answer 27

that 5-1 turns into 4, but you cannot add it to 7 to get 11

Answer 28

f(5) happens when n = 5

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

f(5) = f(1) + f(2) + f(5 - 1) ... replace all copies of n with 5

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

Answer 29

you need to replace f(4) with what we just found f(4) to be

Answer 30

f(5)=2+5+19
f(5)=26

Answer 31

good

Answer 32

thx

Answer 33

np

Answer 34

help me with another

Answer 35

sure, i can do one more

Answer 36

Use the graph below to fill in the blank with the correct number.

f(0) = _______

Answer 37

f(0) means "f(x) when x = 0"

Answer 38

so you're looking for a point with an x coordinate of zero

Answer 39

f(0) will be the point (0, y) where y = f(0)

Answer 40

so ..

Answer 41

any ideas where this point is?

Answer 42

(0,3)

Answer 43

sorry (3,0))

Answer 44

(0,3) or (3,0) is not a point plotted

Answer 45

(-3,0))

Answer 46

how many points are on this graph?