Question

Determine if -1, 1, 4, 8 is a geometric sequence

Answer 1

The sequence is not a geometric sequence

Explanation:

In a geometric sequence you find the following term multiplying the current by a fixed quantity called the common ratio.

To prove if a sequence is geometric we need to check if the ratio is consistent across the sequence. To check for the ratio we use the formula:

`r=(a_n)/(a_(n-1))`

were

`r` is the ratio

`a_n` is the current term

`a_(n-1)` is the previous term

Let's star with 1, so
`a_n=1` and
`a_(n-1)=-1`

`r=(a_n)/(a_(n-1))`

`r=(1)/(-1)`

`r=-1`.

Now let's check 4 and 1, so
`a_n=4` and
`a_(n-1)=1`

`r=(a_n)/(a_(n-1))`

`r=(4)/(1)`

`r=4`

Since the ratios between two pair of numbers are different, we can conclude that the sequence is not geometric.

Answer 2

No, because there is no common ratio

EXPLANATION

The given sequence is

-1, 1, 4, 8

If this sequence is geometric, then there should be a common ratio among the consecutive terms.

`(1)/( - 1) \\e (4)/(1) \\e (8)/(4)`

Hence the sequence

-1, 1, 4, 8

is not a geometric sequence.