Question

Please help me ASAP!!!!!!!!

Answer 1

A sequence is arithmetic if the subtraction between any pair of consecutive terms is constant.

A sequence is arithmetic if the ratio between any pair of consecutive terms is constant.

Let's pick consecutive couples and check their difference and ratio:

First couple: first and second term

Difference: $0 - (-2) = 0+2 = 2$

Ratio: $\frac{0}{-2} = 0$

Second couple second and third terms:

Difference: $2 - 0 = 2$

Ratio: $\frac{2}{0} = \text{undefined}$

So, we can see that the difference remained constant (is always 2), while the ratio isn't even defined. So, this is an arithmetic sequence.

As a corollary, you can see that a geometric sequence can never contain 0. Otherwise, when checking consective ratios, that 0 will eventually be a denominator and break the procedure.