Answer
Neither arithmetic nor geometric
Work Step by Step
We are given the sequence:
$1,1,2,3,5,8,......$
Compute the difference between two consecutive terms:
$1-1=0$
$2-1=1$
$3-2=1$
$5-3=2$
$8-5=3$
As the difference between any consecutive terms is not constant, the sequence is not arithmetic.
Compute the ratio between two consecutive terms:
$\dfrac{1}{1}=1$
$\dfrac{2}{1}=2$
$\dfrac{3}{2}$
$\dfrac{5}{3}$
$\dfrac{8}{5}$
As the ratio between consecutive terms is not constant, the sequence is not geometric.
So the sequence is neither arithmetic nor geometric.