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Thread: 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
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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 $\displaystyle \{a_i,\ i=1,2,..\}$, and $\displaystyle a_{13}=4$ and $\displaystyle a_{21}=8$. What is $\displaystyle a_5\ ?$

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

    So:

    $\displaystyle a_{13}=a_1+12d=4$

    and:

    $\displaystyle a_{21}=a_1+20d=8$

    Subtracting the first of these from the second gives:

    $\displaystyle 8d=4$, so $\displaystyle d=1/2$.

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

    So:

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

    RonL
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