Answer
Neither arithmetic nor geometric
Work Step by Step
We are given the sequence:
$1,3,6,10,......$
Compute the difference between two consecutive terms:
$3-1=2$
$6-3=3$
$10-6=4$
As the difference between any consecutive terms is not constant, the sequence is not arithmetic.
Compute the ratio between two consecutive terms:
$\dfrac{3}{1}=3$
$\dfrac{6}{3}=2$
$\dfrac{10}{6}=\dfrac{5}{3}$
As the ratio between any consecutive terms is not constant, the sequence is not geometric.
So the sequence is neither arithmetic nor geometric.