Question

2, 6, 10, 15, ... O Arithmetic O Geometric O Neither 

Answer 1

Given:

The sequence is:

2, 6, 10, 15,...

To find:

Whether the given sequence is Arithmetic, Geometric, Neither.

Solution:

We have,

2, 6, 10, 15,...

Different between consecutive terms are:

$6-2=4$

$10-6=4$

$15-10=5$

Since $4\neq 5$, therefore the given sequence has no common difference. It means it is not an arithmetic sequence.

Ratio of consecutive terms are:

$\dfrac{6}{2}=3$

$\dfrac{10}{6}=\dfrac{5}{3}$

Since $3\neq \dfrac{5}{3}$, therefore the given sequence has no common ratio. It means it is not a geometric sequence.

Since the given sequence is neither arithmetic nor geometric, therefore the correct option is C.