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Math Help - Arithmetic sequence

  1. #1
    Junior Member
    Joined
    Sep 2009
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    61

    Arithmetic sequence

    find a formula for an for the arithmetic sequence.

    a1=5 , a4=15

    ok this is what i did.

    an=dn+c and c=a1-d

    c=5-d

    how do i find d and c???
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  2. #2
    Super Member
    Joined
    Aug 2009
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    Israel
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    a_n = (n-1)d + a_1

    a_1 = 5, a_4 = (4-1)d + a_1 = (4-1)d + 5 = 15 \Rightarrow 3d + 5 = 15 \Rightarrow 3d = 10 \Rightarrow d = \frac{10}{3}

    Therefore,

    a_n = \frac{10}{3} \cdot (n-1) + 5

    Or in the form you're asked to give:

    a_n = \frac{10}{3} \cdot (n-1) + 5 = \frac{10}{3}n - \frac{10}{3} + 5 = \frac{10}{3}n + \frac{5}{3}

    a_n = \frac{10}{3}n + \frac{5}{3}
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