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

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Answer 1 · 2015-06-27T07:06:19

The sequence is a geometric sequence.

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.