Question

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

Answer 1

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.