Describe the pattern. problem #39: 5, 7.5, 11.25, 16.875. .

This pattern is clearly a geometric sequence because it does not have a common difference. Remember that an arithmetic sequence only occurs if one number goes to the next by either adding or subtracting by the same value.

An example of an arithmetic sequence is 3, 8, 13, 18,...
The sequence or pattern has a common difference of 5.

A geometric sequence goes from a number to the next by either multiplying or dividing by the same value.

So, in order to figure out the pattern we have to find the common ratio (what we multiply the numbers by to continue the pattern).

5x = 7.5

x = 1.5

7.5x = 11.25

x = 1.5

11.25x = 16.875

x = 1.5

Solution: The pattern is a geometric sequence. In order to go from one term to the next, each term needs to be multiplied by 1.5.