Question

Is the following sequence is arithmetic: 2, -2, 2, -2, 2,… ?

Answer 1

The common difference between a pair of terms is not equal, so it can be concluded that the sequence is not an arithmetic sequence.

Explanation:

The sequence provided is
`2,-2,2,-2,2...`

In an arithmetic sequence there is a common difference `d` maintained between any two consecutive terms:

`d_1 = a_2 -a_1`
`d_1 = -2-2`
`color(blue)(d_1 = -4`

`d_2 = a_3-a_2`
`d_2 = 2-(-2)`
`color(blue)(d_2 = 4`

The common difference between the pair of terms is not equal
`color(blue)(d_1 !=d_2`
Hence it can be concluded that the sequence is not an arithmetic sequence.

It does, however, have a common ratio between successive terms, namely `-1`, so it is a geometric progression.