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    Definitions : Sequence, Geometric Progression, String, Recursive

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    1. Sequence
    2. Geometric Progression
    3. String
    4. Recursive definition of a function
    5. Recursive definition of a set
    6. Recursive algorithm
    7. Program correctness
    8. Loop invariant
    9. Final assertion

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    https://brainmass.com/math/computing-values-of-functions/definitions-sequence-geometric-progression-string-recursive-57525

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    On the following terms could you please give my an English text description - in your own words. Thanks.

    1. Sequence
    2. Geometric Progression
    3. String
    4. Recursive definition of a function
    5. Recursive definition of a set
    6. Recursive algorithm
    7. Program correctness
    8. Loop invariant
    9. Final assertion

    Sequence: In mathematics, a sequence is a list of objects (or events) arranged in a "linear" fashion, such that the order of the members is well defined and significant.

    In other words, a sequence can be defined by a function f: N  S, where N is set of natural numbers and S is any abstract set.

    With f(1) = f1, f(2) = f2, ......... f(n) = fn
    And the sequence is represented as: {f1,f2,f3,.........fn}

    NOTE: If the letter n is finite, then the sequence is called as finite sequence, otherwise if n is infinite, and then the sequence is an infinite sequence.

    Geometric progression: It is also called as geometric sequence, which is a sequence of numbers such that the quotient of any two successive members of sequence is a constant called common ratio of the sequence.

    Thus, we have a geometric sequence written as

    a1 = ar0, a2 = ar1, a3 = ar2,........., an = arn-1......, where r is the common ratio, a ...

    Solution Summary

    Definitions of Sequence, Geometric Progression, String, Recursive definition of a function, Recursive definition of a set, Recursive algorithm, Program correctness, Loop invariant, Final assertion are provided. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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