How do you determine if -10,20,-40,80 is an arithmetic or geometric sequence?

1 Answer
Jun 27, 2015

The sequence is a geometric sequence.

Explanation:

  • In an Arithmetic sequence there is a common difference #d# between any two consecutive terms
  • In a Geometric sequence there is a common ratio #r# for any two consecutive terms

The sequence given is :

#-10, 20 , -40, 80#

1) Checking if the sequence is an arithmetic sequence:

# color(blue)(d _1= a_2 - a_1) = 20 - (-10) = color(blue)(30#
# d_2 = a_3 - a_2 = -40 - (20) =color(blue)( -60#

As observed #d_1 != d_2# , so it is not an arithmetic sequence.

2) Checking if the sequence is a geometric sequence:

# color(blue)(r _1= a_2/ a_1) = 20 / -10 = color(blue)(-2#

# color(blue)(r _2 = a_3/ a_2) = (-40 )/ 20 = color(blue)(-2#

# color(blue)(r _3 = a_4/ a_3) = (80 )/-40 = color(blue)(-2#

Since #r_1 = r_2 = r3# it forms a geometric sequence.

So the sequence is a geometric sequence.