Geometric Sequences

Geometric Sequences - are sequences that multiply or divide by a constant amount every step.

Examples of Geometric Sequences are shown below:

2, 4, 8, 16

5, 2.5, 1.25, .625

8, 24, 72, 216

Each of these sequences is multiplying or dividing by the same amount every step. This common multiplication/division is called the Multiplier. We refer to the multiplier as r. To find the multiplier of a geometric sequence we can divide the second value by the first value.

For example, the first sequence's difference is 4/2 = 2.

The multiplier for the 3 sequences above is shown below:

sequence 1 has a multiplier of 2

sequence 2 has a multiplier of 1/2

sequence 3 has a multiplier of 3

Try finding the common difference for each of these sequences:

7, 1.75, .4375, .109375

1, 9, 81, 729

2, 8, 32, 128

The position of a geometric sequence is represented by the letter n. The value of the sequences at position n is an.

The table above is a table of sequence 1 above. We can see that the common difference of the value is 2. The only difference is that this table displays the position of the value in the sequence. So, at position n = 1, we can see that the value of an, or the value in position 1 is 2. In position 2, the value of an is 4.

The last important piece of information is the starting value of the sequence. The starting point is referred to as a1. The starting point of the table above is where n = 1. The value of an is 2. So, the starting point of our geometric sequence is 2.