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

Question

Trace Arias · Accepted Answer

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} \neq d_{2}

, so it is not an arithmetic sequence.

2) Checking if the sequence is a geometric sequence:

r_{1} = \frac{a_{2}}{a_{1}} = \frac{20}{- 10} = - 2

r_{2} = \frac{a_{3}}{a_{2}} = \frac{- 40}{20} = - 2

r_{3} = \frac{a_{4}}{a_{3}} = \frac{80}{- 40} = - 2

Since

r_{1} = r_{2} = r 3

it forms a geometric sequence.

So the sequence is a geometric sequence.

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

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