Question

Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 125, 25, 5, .. ..​

Answer 1

Answer:

this is a geometric sequence and the common ratio is equal to 1/5.

Step-by-step explanation:

Answer 2

Answer:

Given sequence is an arithmetic sequence.

Step-by-step explanation:

Given sequence is:

125, 25, 5, .. ..​

Here

$a_1 = 125\\a_2 = 25\\a_3 = 5$

• A sequence is geometric sequence when the common ratio of consecutive terms is same. It is denoted by r.

• A sequence is an arithmetic sequence when the common difference of consecutive terms is same. It is denoted by d.

Finding the common ratio

$r = \frac{a_2}{a_1} = \frac{125}{25} = 5\\r = \frac{a_3}{a_2} = \frac{25}{5} = 5$

As we can see that the common ratio is same, the given sequence is a geometric sequence.