Question

Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 5, 15, 45,

Answer 1

To answer this question, we need to check the sequence and find the common difference for an arithmetic sequence, or a common ratio for a geometric sequence.

Let us check if the sequence is arithmetic:

`15-5=10,45-15=30`

There is not a common difference in this case.

Then, we need to check if we have a common ratio. For this, we need to divide the second term of the sequence by the first term of the sequence, and check if this rule applies for the next terms of the sequence:

`(15)/(5)=3,(45)/(15)=3`

Therefore, we have a geometric sequence, and the common ratio is r = 3.