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

Aug 10, 2015

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

${d}_{2} = {a}_{3} - {a}_{2}$
${d}_{2} = 2 - \left(- 2\right)$
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.