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    How to get the formula for Sn of an arithmetic series?

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    Tn = a+(n -1)d

    sn = n/2(a + n)

    4. For the series 3 + 9 + 15 + 21... Find:
    a) an expression for tn
    b) an expression for sn
    c) the answer if s = 20
    d) the answer if t = 115

    5. Find the # of terms in the sequencece 2,6,10... 626

    I need a step by step procedure for solving these problems.

    © BrainMass Inc. brainmass.com December 24, 2021, 4:44 pm ad1c9bdddf
    https://brainmass.com/math/algebra/get-formula-arithmetic-series-5082

    SOLUTION This solution is FREE courtesy of BrainMass!

    4. In this series a=3, d=6. So
    <br> a) tn=3+(n-1).6=6n-3
    <br> b) sn=n(3+n)/2
    <br> c) if s=20, then n(n+3)/2=20, that is, n^2+3n-40=0.
    <br> So n=5 or n=-8(discard). So n=5.
    <br> d) If t=115,
    <br> I am not sure if you state problem correctly, whether "t" is the same as tn, if so, there will not exist an n such that tn=115.
    <br>
    <br>5. In this sequence 2,6,10,...,626, a=2, d=4, and a(n)=626.
    <br> So you can use a(n)=a+(n-1)d=4n-2=626
    <br> Thus, n=628/4=157
    <br>

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:44 pm ad1c9bdddf>
    https://brainmass.com/math/algebra/get-formula-arithmetic-series-5082

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