Question

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

Answer 1

Answer:

The sequence is not a geometric sequence

Step-by-step 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:

$r=\frac{a_n}{a_{n-1}}$

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 $a_{n-1}=-1$

$r=\frac{a_n}{a_{n-1}}$

$r=\frac{1}{-1}$

$r=-1$.

Now let's check 4 and 1, so $a_n=4$ and $a_{n-1}=1$

$r=\frac{a_n}{a_{n-1}}$

$r=\frac{4}{1}$

$r=4$

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

Answer 2

ANSWER

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.

$\frac{1}{ - 1} \ne \frac{4}{1} \ne \frac{8}{4}$

Hence the sequence

-1, 1, 4, 8

is not a geometric sequence.