figuring out the number of bugs in the next generation

[colinjohnedwards]

:?: please help i told my girfriend that i would help her with this but i dont understand how to do it, all i could do was work out a patern to find the next genreation of bugs please help im sure that its simple but the more i study it the more strest im geting ive been on it most of the day the question is.......

There is a red bug, the red bug produces 1 red an 1 yellow bug
the new red bug produces 1 red an 1 yellow bug and the yellow produces a red bug and so on

i need to work out a way of working out how many of the 20th generation of bugs there will be with out drawing loads of red and yellow bugs on the paper

i did work this out but it doesnt realy help much as it needs to be simple like red * x + sothing = ans please help as i told her that i will work it out so she can conontrate on the rest of her corse work :?

 

[tkhunny]

Are you sure it's worth it? Sometimes, it helps to invent a code or shorthand.

1) R - R1

2) RY - R1Y1

3) RYR - R2Y1

Get the idea? This is a generation at a time, not the total of all generations.

4) R2Y2R1 = R3Y2

5) R3Y3R2 = R5Y3

6) R5Y5R3 = R8Y5

I'm seeing a regular pattern. How about you?

 

[colinjohnedwards]

thanks, yes i see the patern

1st gen) 1R 0y = 1 bug
2nd gen) 1R 1y = 2 bug
3rd gen) 2R 1y = 3 bug

i worked out that if i wanted to find 4th gen i add 3rd gens 2R & 1y together to make 3 which will be the red or R for 4th gen

4th gen) 3R __y = bug an to get total number of bugs i add
3rd gen and 4th gen total together to make 5 bug
then i can take the 3r from the 5 bug to get the y which is 2
so 4th gen is 3R 2Y = 5 bug
but is there a way of working it out with out having to write out each gen
so i could just say how much 10th gen will be with out knowing the 9th an 8th
thanks
oh em do you know what subject this is what form of maths thanks ,colin