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

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 ${d}_{1} \ne {d}_{2}$ , 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 ${r}_{1} = {r}_{2} = r 3$ it forms a geometric sequence.

So the sequence is a geometric sequence.