A

geometric series is one where each term is generated by applying a

multiplier to the last. This is a geometric series with common difference *2 -

2 + 4 + 8 + 16 + 32

If we want to find the sum of this series (the sum is the total of all the terms added together), we use the following formula -

r^{n} - 1
a * -----------------
r - 1

Where a is the first term, r is the common ratio, and n is the number of terms.

**Example 1**

Sum the series 2 + 6 + 18 + 54 + ... (8 terms).

First term = 2

Common difference = 3

Number of terms = 8

2 * ((3^{8} - 1)/(3 - 1)) = 6560.

**Example 2**

Sum the series 8 + 4 + 2 + 1 + 0.5 + ... (10 terms)

First term = 8

Common difference = 0.5

Number of terms = 10

8 * ((0.5^{10} - 1)/(0.5 - 1)) = 15.984

Note how geometric series which involve division can be modelled by substituting the appropriate fraction - dividing by 2 is the same as multiplying by 0.5.