## anonymous 3 years ago What is the n th term of the series: 1+1+2+3+5+8+13+21+...

1. anonymous

A(n) = A(n-1) + A(n-2) where a1 = 1 and a2 = 1 ?

2. anonymous

In terms of n

3. anonymous

Looks familiar....

4. anonymous

N th term is given by the formulae A(n)=A(n+1)+A(n+2) N=(n+1)+(n+2)

5. anonymous

???

6. anonymous

I know |dw:1350296451209:dw|

7. anonymous

But what in terms of n only.

8. anonymous

it's funny that there is a question about the golden ratio now

9. anonymous

it is fibonacci...

10. anonymous

Yes

11. anonymous

In terms of n ----> FIBOnnACCI

12. anonymous

$F_n-F_{n-1}-F_{n-2}=0 \ \ \ n\ge2$ setting up characterestic equation gives$\lambda^2-\lambda-1=0$wchich gives$\phi_1=\frac{1+\sqrt{5}}{2}$$\phi_2=\frac{1-\sqrt{5}}{2}$and so$F_n=A\phi_1^n+B\phi_2^n$and all u need is finding A and B using the values of $$F_0$$ and $$F_1$$

13. anonymous

finally

14. anonymous

@mukushla how |dw:1350297426979:dw|

15. anonymous

oh I get it now...... thanx

16. anonymous

@sauravshakya may you explain how ?

17. anonymous

i thought i got it but i realized that i was wrong

18. anonymous

ok got it .. nvm :)