Question

FAN AND MEDAL:


Generate the first 5 terms of this sequence:

f(1) = 0 and f(2) = 1, f(n) = f(n - 1) + f(n - 2), for n > 2

Answer 1

@mustafa2014 @hartnn

Answer 2

Okay:

try putting n = 3 in the given equation.

Answer 3

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

Answer 4

good so,

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

Now you already know f(1) and f(2). So, plug in the values and find out f(3).

Answer 5

Can you tell me what do you obtain ?

Answer 6

f(3) = f(2) + f(1) = 0 + 1
f(3) = 0 + 1 = 1
f(3) = 1 = 1 ?????

Answer 7

Great !

Now similarly find out f(4) and tell me its value. Remember now you have f(1),f(2) and f(3) already known so you can use their values as and when necessary.

Answer 8

f(4) = 2 ?

Answer 9

great work

now f(5) ?

Answer 10

f(5) = 4

Answer 11

How ?

Answer 12

sorry, i meant to put 3

Answer 13

wait, its 2 isnt it?

Answer 14

@kaylamarie101
write f(5) in terms of f(n-1) and f(n-2), first. What do you get?

Answer 15

ugh, im lost again. It'd be f(4) + f(3) + f(2) + f(1)
So, 2 + 1 + 0 +1..so wouldn't I have been right the first time?

Answer 16

No No

Answer 17

See:

for obtaining f(3) I asked you to put n = 3 and you did the same.

for obtaining f(4), put n = 4, you will get:

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

Now you had already calculated f(3) and f(2) was given to you so you had to just plug in those values to get the value of f(4).

Do you understand this ?

Answer 18

Yes, And I got f(4)...so would it now be:
f(5)= f(5-1) + f(5-2) = f(4) + f(3) ?

Answer 19

perfect !!

Answer 20

Now tell me value of f(5).

Answer 21

Okay, so:
f(5)= f(4) + f(3) = f(4) + f(3)
f(5) = 2 + 1 = 2+1
f(5) = 3 = 3
So, f(5) = 3
Which then means that the answer to the original problem is:
0, 1, 1, 2, 3 Right? (:

Answer 22

@vishweshshrimali5

Answer 23

You are correct. But, as @hartnn pointed out a mistake: the sequence says n>2, so, the first 5 terms would be f(3), f(4),..f(7).

So, you just have to calculate f(6) and f(7) also.

Answer 24

Okay, f(6) = f(6-1) + f(6-2) = f(5) + f(4)
f(6) = f(5) + f(4)
f(6) = 3 +2 = 5

Answer 25

Good

Answer 26

f(7) = f(7-1) + f(7-2) = f(5) + f(6)
f(7) = f(6) + f(5) = f(5) + f(6)
f(7) = 5 + 3= 8
f(7) = 8

Answer 27

Great work

Answer 28

So your required answer is ?

Answer 29

I'm unsure...where do I go from here?

Answer 30

See, the question asks for first 5 terms and they would be f(3),f(4),f(5),f(6),f(7).

So, in place of f(...), write its value and that's your final answer.

Answer 31

Okay! I get it now...So, it would be:
1, 2, 3, 5, 8

Answer 32

Good

Answer 33

Awesome! Thanks so much! :D

Answer 34

no problem and keep this great work.