Question

How do you tell whether the sequence -8, 24, -72.... is arithmetic, geometric, or neither?

Answer 1

The sequence is a geometric sequence.

Explanation:

`-8,24,-72...`

• Checking if it a geometric sequence :

In a geometric sequence a common ratio `r` is constantly maintained between any two consecutive terms.

`r` is obtained by dividing a term by its preceding term

`r_1= 24/-8= -3`

`r_2= -72/24 = -3`

Since `r_1= r_2` this shows that the ratio maintained is constant, so the sequence is geometric in nature.

• Checking if the sequence is an arithmetic progression:

For an arithmetic progression a common difference `d` is maintained between two consecutive terms.

`d_1=24-(-8) = 24+8=32`

`d_2=-72-24=-96`

Since `d_1 != d_2` the sequence is not an arithmetic sequence.