fibonacci! how many pairs of rabbits would there be after one year?

Question

233
377 ............???

since no-one is answering...

the fibonacci sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 etc etc

so would the number after a year be the 12th number or the 13th number?

started with one

and reproduce once a month =)

Answer 1

That is quite a cryptic question... let's see if I can guess...
Every pair of rabbits produce one new pair of offspring every month, except in their first year; starting with one pair at time zero, we get the sequence
F(0) = 1
F(1) = 1
F(2) = 2
F(3) = 3
F(4) = 5
F(5) = 13
F(6) = 21
F(7) = 34
F(8) = 55
F(9) = 89
F(10) = 144
F(11) = 233
F(12) = 377 (after one year)
F(13) = 610
F(14) = 987
... every number is equal to the sum of the two previous numbers.

A nice little trick: if n is two more than the number of the month, calculate

1.6180339887^n and
(-0.6180339887)^n

Subtract the two outcomes and divide the difference by
2.2360679775 (or by sqrt 5).

In this case, if n = 14,
... 1.6180339886^14 = 842.9988
... (-0.6180339886)^14 = 0.0012
Subtracted, they make 842.9976; divide by the square root of 5:
... 842.9976 / 2.2360679775 = 377.

Answer 2

F(0) = 1
F(1) = 1
F(2) = 2
F(3) = 3
F(4) = 5
F(5) = 8
F(6) = 13
F(7) = 21
F(8) = 34
F(9) = 55
F(10) = 89
F(11) = 144
F(12) = 233 (after one year) but ignoring the F(0), then, it is the F(13)=377 as the answer

Answer 3

Just sum up the sequence and you have the total number after one year.

Answer 4

Gotta know how many you started with, and how often they reproduce ☺

Doug

Answer 5

Depends on how often they give birth and how many in each litter.