Question

Tell whether the sequence is arithmetic. If it is, identify the common difference and write the explicit formula. Please show detailed steps: 2, -1, 5,-4,......

Answer 1

Answer: The sequence is not Arithmetic.

Step-by-step explanation:

It is important to remember that,  by definition, a sequence is Arithmetic when the difference between each term is constant (this difference is called the "Common difference" as it is represented with "d")

Knowing this and given the following sequence provided in the exercise:

$2, -1, 5,-4,...$

You need to find the differences of the consecutive terms. You get that:

$-1-2=-3\\\\5-(-1)=6\\\\-4-5=-9$

Therefore, since the differences between the consecutive terms is not constant, you can conclude that the given sequence is not Arithmetic.