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2. Arithmetico-geometric sequence - Wikipedia

   en.wikipedia.org/wiki/Arithmetico-geometric_sequence

   The nth element of an arithmetico-geometric sequence is the product of the nth element of an arithmetic sequence and the nth element of a geometric sequence. [1] An arithmetico-geometric series is a sum of terms that are the elements of an arithmetico-geometric sequence. Arithmetico-geometric sequences and series arise in various applications ...

3. Geometric progression - Wikipedia

   en.wikipedia.org/wiki/Geometric_progression

   For example, the sequence 2, 6, 18, 54, ... is a geometric progression with a common ratio of 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with a common ratio of 1/2. Examples of a geometric sequence are powers r k of a fixed non-zero number r, such as 2 k and 3 k. The general form of a geometric sequence is

4. Arithmetico–geometric series - Wikipedia

   en.wikipedia.org/?title=Arithmetico–geometric...

   Download as PDF; Printable version; From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Arithmetico-geometric sequence; Retrieved from " ...

5. Arithmetic–geometric mean - Wikipedia

   en.wikipedia.org/wiki/Arithmetic–geometric_mean

   The geometric mean of two positive numbers is never greater than the arithmetic mean. [3] So the geometric means are an increasing sequence g 0 ≤ g 1 ≤ g 2 ≤ ...; the arithmetic means are a decreasing sequence a 0 ≥ a 1 ≥ a 2 ≥ ...; and g n ≤ M(x, y) ≤ a n for any n. These are strict inequalities if x ≠ y.

6. Arithmetic geometry - Wikipedia

   en.wikipedia.org/wiki/Arithmetic_geometry

   In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. [1] Arithmetic geometry is centered around Diophantine geometry , the study of rational points of algebraic varieties .

7. Wheat and chessboard problem - Wikipedia

   en.wikipedia.org/wiki/Wheat_and_chessboard_problem

   The exercise of working through this problem may be used to explain and demonstrate exponents and the quick growth of exponential and geometric sequences. It can also be used to illustrate sigma notation. When expressed as exponents, the geometric series is: 2 0 + 2 1 + 2 2 + 2 3 + ... and so forth, up to 2 63. The base of each exponentiation ...