If the tenth number of a Fibonacci type sequence is 322, then what are the first nine numbers?

Question

i dont know what the formula is to do fibonaaci sequences so if you could explain that to me i would appreciate it

Answer 1

Let the first two terms of your mystery sequence be , a and b. Adding these in the
fibonacci manner ,

a,b,a+b,a+2b,2a+3b,3a+5b,5a+8b,8a+13b,

13a+21b, and the tenth term is 21a+34b.

Then, 21a + 34b = 322 = 2(7)(43).

Since 2 divides 34 ,2 must divide 21a and so

2 divides a. Similarly, 7 divides b. Since the tenth term of 2,7,... is 280 , we pick the next
multiple of 2 for the first term:

4,7,11,18,29,47,76,123,199,322.

Answer 2

Suppose the sequence you're looking for starts like so:
s(1) = a
s(2) = b
s(n) = s(n-2) + s(n-1)

If you write out what s(3), s(4) and such are in terms of a and b, you'll see that

s(n) = f(n-2)a + f(n-1)b,

where f(n) is the fibonacci sequence given by:

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

f(8) = 21, f(9) = 34

so we have: 21a + 34b = 322

assuming you want a and b to be integers, this is an example of a Diophantine equation. If you haven't studied these, then you can just solve for b and then plug in a = 1, 2, 3, ... until you get a whole number for b.

I get a solution of a = 4, b = 7. Then the sequence is

4, 7, 11, 18, 29, 47, 76, 123, 199, 322, ...

Answer 3

the fibonacci sequence starts with 0,1. the third term is found by adding these two terms and each following term follows those rules:
0,1,1,2,3,5,8,13,21,34,56,90,146,236,382...

your tenth number is 322 so you need to look for two numbers that total 322 and work back from there. is there any suggestion given as to the starting number? if not then you could assume any two numbers, eg 200 and 122, working back from there you would get 78 (200-122), 44 (122-78), 34, 10, 24, -14, 38
weird...
you may need to play around a bit to get a sequence that increases each time.
an interesting question.

Answer 4

The Fibonacci series is formed by starting with 0 and 1 and then adding the latest two numbers to get the next one:

0 1 --the series starts like this.
0+1=1 so the series is now
0 1 1
1+1=2 so the series continues...
0 1 1 2 and the next term is
1+2=3 so we now have
0 1 1 2 3 and it continues

Answer 5

Evolution believes that in spite of trait helps a specie proceed to exist is the trait which will stick around. The series is probable the main suitable way for species to improve because nature do tend to take the course with least resistance. i don't see how this conflicts with evolution. in reality, because of the fact it quite is barely latest in some species and not others is evidence that not each thing grew to become into created out of a similar mildew. in spite of if it quite is, as you declare, to be God's variety, then what do you call those that did not endure the sequency?