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

Jackson Garner

Jackson Garner

Answered question

2022-09-24

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

Answer & Explanation

Trace Arias

Trace Arias

Beginner2022-09-25Added 6 answers

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:

d 1 = a 2 - a 1 = 20 - ( - 10 ) = 30
d 2 = a 3 - a 2 = - 40 - ( 20 ) = - 60

As observed d 1 d 2 , so it is not an arithmetic sequence.

2) Checking if the sequence is a geometric sequence:

r 1 = a 2 a 1 = 20 - 10 = - 2

r 2 = a 3 a 2 = - 40 20 = - 2

r 3 = a 4 a 3 = 80 - 40 = - 2

Since r 1 = r 2 = r 3 it forms a geometric sequence.

So the sequence is a geometric sequence.

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