If a is any number, the sequence {a, a, a, a, ...} is called a constant sequence.?

Explain why a constant sequence is both arithmetic and geometric.

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  • 8 years ago
    Best Answer

    Hi Ben,

    Recall the definitions for arithmetic and geometric sequences. Arithmetic sequences require that the common difference between consecutive terms is constant. Geometric sequences, on the other hand, require that the common ratio between consecutive terms be constant.

    So in your question, you have a constant sequence which means that the terms are unchanging. To consider whether the constant sequence is arithmetic, calculate the difference between any successive terms: a - a = 0. Because that will be the difference between any two consecutive terms, there is a common difference between consecutive terms, and the constant sequence is arithmetic.

    To consider whether the constant sequence is geometric, calculate the ratio between any successive terms: a/a = 1 (assuming a != 0). Because this is ratio of any two consecutive terms, there is a common ratio between consecutive terms, and the constant sequence is geometric, provided a != 0.

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  • Melvyn
    Lv 7
    8 years ago

    in the case of an arithmetic sequence the constant difference d =0 , in the case of geometric sequence the constant ratio r would be equal to 1

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