Question

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

Answer 1

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

Answer 2

In terms of n

Answer 3

Looks familiar....

Answer 4

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

Answer 5

???

Answer 6

I know

Answer 7

But what in terms of n only.

Answer 8

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

Answer 9

it is fibonacci...

Answer 10

Yes

Answer 11

In terms of n ----> FIBOnnACCI

Answer 12

\[F_n-F_{n-1}-F_{n-2}=0 \ \ \ n\ge2\]
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 \(F_1\)

Answer 13

finally

Answer 14

@mukushla how