Question

What is the common ratio of the sequence? -2,6,-18,54

Answer 1

ANSWER

The common ratio is -3.

EXPLANATION

In general, the common ratio of a Geometric Sequence is given by:

$r = \frac{a_{n+1}}{a_{n}}$

We can find the common ratio using any two consecutive terms of the geometric sequence by dividing the subsequent term by the previous term.

The given sequence is -2,6,-18,54

Using the first two terms the common ratio is

$r = \frac{6}{ - 2} = - 3$

We could also used the second and third terms to get

$r = \frac{ - 18}{6} = - 3$

and so on and so forth.

Therefore the common ratio is -3.