Question

Which is true regarding the sequence below?

5,2,-3,-10,-19

A. The sequence is arithmetic because the common difference is -1.
B. The sequence is arithmetic because the common difference is 1.
C. The sequence is not arithmetic because there is no common difference. The differences are -3,-5,-7 and-9.
D. The sequence is not arithmetic because there is no common difference. The differences are -1/3,-1/5,-1/7 and -1/9

Answer 1

It is not an arithmetic sequence because the difference between each term is not the same.
5 - 3 = 2
2 - 5 = -3
-3 - 7 = -10
-10 - 9 = -19
The differences are: -3, -5, -7, -9
The answer is LETTER C

Answer 2

Option C is correct.The sequence is not arithmetic because there is no common difference. The differences are -3,-5,-7 and-9.

Explanation:

We have given the sequence 5,2,-3,-10,-19

Common difference of arithmetic sequence is
`d=a_2-a_1`

we can see the difference between all the terms are d=2-5=-3 here
`a_2=2,a_1=5`

`d=-3-2=-5` here
`a_2=-3,a_1=2`

`d=-10-(-3)=-7` here
`a_2=-10,a_1=-3`

`d=-19-(-10)=-9` here
`a_2=-19,a_1=-10`

Therefore, this is not an arithmetic because there is no common difference.Differences are -3,-5,-7 and-9.