General term of the sequence -1/2, 1, -7/8, 10/6...?

Anybody see a pattern?

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  • 8 years ago
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    If the last term is actually 10/16 rather than 10/6, then here is the pattern:

    Rewrite the second term as 4/4.

    Then the sequence is -1/2.4/4,-7/8,10/16, ...

    The numerators form an arithmetic sequence 1, 4, 7, 10, ... with a common difference of 3. The general term for the numerators can be found using the formula a+(n-1)(d) where a is the first term.

    So for the numerators, the general term is

    1+(n-1)(3)

    =1+3n-3

    =3n-2

    The denominators form a geometric sequence -2, 4, -8, 16, ...with common ratio r =-2.

    The general term of a geometric sequence can be found using the formula ar^(n-1).

    So for the denominators, the general term is

    (-2)(-2^(n-1))

    Putting this together, the general term for your sequence is

    (3n-2)/(-2)(-2^(n-1))

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