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

1 Answer

Answer:

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.