« Arithmetic Progressions 

By a geometric progression of m terms, we mean a finite sequence of the form
The real number a is called the first term of the geometric progression, and the real number r is called the ratio of the geometric progression.
Example 1:
Consider the finite sequence of numbers
4, 8, 16, 32, 64, 128, 256, 512, 1024
This sequence has the property that the ratio between successive terms is constant and equal to 2.
Here we have: a = 4; r = 2.
the kth term of the geometric progression is equal to
The sum of the m terms of a geometric progression is equal to
Example 2:
Consider the geometric sequence
Here we have: a = 1, r =
The sum of the first m terms is equal to
This is very close to 2 when m is very large.