How do you tell whether the sequence -8, 24, -72.... is arithmetic, geometric, or neither?

1 Answer
Oct 22, 2015

Answer:

The sequence is a geometric sequence.

Explanation:

#-8,24,-72...#

  • Checking if it a geometric sequence :

In a geometric sequence a common ratio #r# is constantly maintained between any two consecutive terms.

#r# is obtained by dividing a term by its preceding term

#r_1= 24/-8= -3#

#r_2= -72/24 = -3#

Since #r_1= r_2# this shows that the ratio maintained is constant, so the sequence is geometric in nature.

  • Checking if the sequence is an arithmetic progression:

For an arithmetic progression a common difference #d# is maintained between two consecutive terms.

#d_1=24-(-8) = 24+8=32#

#d_2=-72-24=-96#

Since #d_1 != d_2# the sequence is not an arithmetic sequence.