A sequence of numbers is said to be geometric if any term after the first can be obtained by multiplying the previous number by the same constant. This constant is called the common ratio. So the sequence 1,2,4,8,16 is geometric since each number in the sequence after the first can be obtained by multiplying the previous term by 2. Here the common ratio is 2. A geometric series is the sum of the terms of a geometric sequence. Thus, 1+2+4+8+16 is a geometric series. Geometric series may be finite, such as the series in the preceding sentence, or infinite, such as 1+2+4+..., where the three dots indicate that the series follows this pattern forever. A finite series obviously has a sum, such as 1+2+4+8+16=31. If we write the general finite geometric series as a+ar+ar²+ar³+...+arⁿ=S_n, then it can be shown that S_n=a-arⁿ⁺¹)/(1-r...