Find the Common Ratio of the Sequence. –125, –25, –5, –1, . . .

A sequence in which the ratio between two consecutive terms is the same is called a geometric sequence.

Answer: The common ratio of the sequence –125, –25, –5, –1, . . .  is 1/5.

Let's find the common ratio.

Explanation: 

The common ratio of any geometric progression can be calculated by dividing any two consecutive terms and simplifying it to the simplest form.

⇒ \(a_{2}\) / \(a_{1}\) = -25 / -125 = 1/5

The ratio 1/ 5 is the same in the sequence, hence called the common ratio.

Thus, the common ratio of the sequence –125, –25, –5, –1, . . .  is 1/5.