# What is the common ratio of the geometric sequence: 128, -16, 2, -1/4, …?

##### 1 Answer

Explanation also solves the rest of the sequence structure!

#### Explanation:

where

Let any term in this sequence be

Let a constant be k

let the ratio be r

Two points to note:

Point 1:

it is reducing so

Point 2:

The sequence alternates positive to negative so involves

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider the alternating +ve and -ve

If

if

To find r ignore the

You are not asked to find the value of k.

But you could by

so

for a quick check I select