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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. Arithmetic progression - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_progression

    An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.

  4. Geometric progression - Wikipedia

    en.wikipedia.org/wiki/Geometric_progression

    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 , , , , , … where r is the common ratio and a is the initial value. The sum of a geometric progression's terms is called a geometric series.

  5. Harmonic progression (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Harmonic_progression...

    In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression, which is also known as an arithmetic sequence. Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms.

  6. 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 .

  7. Arithmetic–geometric mean - Wikipedia

    en.wikipedia.org/wiki/Arithmeticgeometric_mean

    In mathematics, the arithmeticgeometric mean (AGM or agM [1]) of two positive real numbers x and y is the mutual limit of a sequence of arithmetic means and a sequence of geometric means. The arithmeticgeometric mean is used in fast algorithms for exponential, trigonometric functions, and other special functions, as well as some ...

  8. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    Regular paperfolding sequence 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, ... At each stage an alternating sequence of 1s and 0s is inserted between the terms of the previous sequence.

  9. Sequence - Wikipedia

    en.wikipedia.org/wiki/Sequence

    Such a sequence is called a singly infinite sequence or a one-sided infinite sequence when disambiguation is necessary. In contrast, a sequence that is infinite in both directions—i.e. that has neither a first nor a final element—is called a bi-infinite sequence, two-way infinite sequence, or doubly infinite sequence.

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