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| « Arithmetic Progressions |
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By a geometric progression of m terms, we mean a finite sequence of the form
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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 k-th term of the geometric progression is equal to
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The sum of the m terms of a geometric progression is equal to

Example 2:
Consider the geometric sequence
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Here we have: a = 1, r =
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The sum of the first m terms is equal to

This is very close to 2 when m is very large.
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