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Math Help - Arithmetic Sequence

  1. #1
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    Arithmetic Sequence

    In Arithmetic sequence
    a13=4;a21=8;a5=?

    What will be the answer?? help
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by machilove
    In Arithmetic sequence
    a13=4;a21=8;a5=?

    What will be the answer?? help
    Lets assume this question is: We have an arithmetic progression \{a_i,\ i=1,2,..\}, and a_{13}=4 and a_{21}=8. What is a_5\ ?

    Given that \{a_i,\ i=1,2,..\} is an arithmetic progression we know that a_n=a_1+(n-1)d, where a_1 is the first term, and d
    is the common difference.

    So:

    a_{13}=a_1+12d=4

    and:

    a_{21}=a_1+20d=8

    Subtracting the first of these from the second gives:

    8d=4, so d=1/2.

    Substituting this value for d back into one of the equations gives a=-2.

    So:

    a_5=-2+4 \times (1/2) =0

    RonL
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