can anyone find the n term in following series?
1,1,2,3,5,8,13,21,34

Question

can anyone find the n term in following series?
1,1,2,3,5,8,13,21,34

anonymous · Answer

its a fibonacci series as it satisfies f(n)=f(n-1)+f(n-2) ...using the formula yu can get the answer

anonymous · Answer

yup i know it. how if one were to find f(n) without finding previous terms?

hartnn · Answer

do u know about golden ratio ?

anonymous · Answer

there is a direct formula for it but it will be difficult to remember

anonymous · Answer

yeah thats why i want to find f(n)

hartnn · Answer

$\Large F_n = \frac{\varphi^n-\psi^n}{\varphi-\psi} = \frac{\varphi^n-\psi^n}{\sqrt 5}$

hartnn · Answer

where, 
$\Large \varphi = \frac{1 + \sqrt{5}}{2} \approx 1.61803\,39887\cdots\,$

hartnn · Answer

and 
$\Large \psi = \frac{1 - \sqrt{5}}{2} = 1 - \varphi = - {1 \over \varphi} \approx -0.61803\,39887\cdots$

anonymous · Answer

seriously ?? well i thought it would be much simpler. Thnks hartnn

hartnn · Answer

yup, the easiest thing is to write it as f(n-1)+f(n-2) :)