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  2. 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

  3. Geometric series - Wikipedia

    en.wikipedia.org/wiki/Geometric_series

    The geometric series is an infinite series derived from a special type of sequence called a geometric progression.This means that it is the sum of infinitely many terms of geometric progression: starting from the initial term , and the next one being the initial term multiplied by a constant number known as the common ratio .

  4. 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 ...

  5. 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 ...

  6. Mirifici Logarithmorum Canonis Descriptio - Wikipedia

    en.wikipedia.org/wiki/Mirifici_Logarithmorum...

    He notes that arithmetic progressions are easy to calculate since they only involve addition and subtraction but that geometric progressions are, in general, harder to compute because they involve multiplication, division and possibly roots.

  7. American Airlines plane narrowly avoids crashing into Hawaii ...

    www.aol.com/american-airlines-plane-narrowly...

    The dramatic elevation gain — which came after the pilot failed to make a turn following takeoff — likely prevented the plane from slamming into the Koʻolau mountain range on the island of ...

  8. Couple Uses Wedding Fund to Pay for Surgery on Injured Dog ...

    www.aol.com/lifestyle/couple-uses-wedding-fund...

    An Arkansas couple has given up their wedding fund to help an injured dog in need. Dylan McCay and his fiancé Emily Roberts revealed they used the money to pay for reconstructive surgery on a ...

  9. Rate of convergence - Wikipedia

    en.wikipedia.org/wiki/Rate_of_convergence

    The staggered geometric progression ... the order of convergence for a sequence generated by a fixed point iteration is to calculate the following sequence, ...

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