Geometric Progression.

The term "geometric progression" refers to a sequence of numbers that can be infinite or can have a fixed number of terms. The numbers after the first term in the sequence are determined by multiplying the previous term by a number called the common ratio. The common ratio of a geometric progression does not change throughout the entire sequence of the series. For example, an infinite geometric progression starting with the number 3 and using a common ratio of 2 would begin in this way: 3, 6, 12, 24, 48, and so on. In other words, the next term in the sequence is determined by multiplying the rightmost term by the value of the common ratio. The start value of the sequence is known as the scale factor; in the preceding example, the scale factor is 3. Thus, the general form of any geometric progression should follow the pattern of a, ar, ar 2, ar 3, ar 4…, where a = the scale factor and r = the common ratio. This presumes that r is not equal to 0. Using these values, it is possible to calculate the nth term of a geometric progression. The formula used to determine the nth value is an = arn-1 .