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Math Help - arithmetic progression

  1. #1
    cpj
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    arithmetic progression

    I need to find first term and common difference for an arithmetic progression where Un denotes the nth term and the sum of the first n terms is denoted Sn.
    I am told U5 + U16 = 44 and that S18=3*S10

    I cant see a way to find either of them... any help please.
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  2. #2
    Senior Member I-Think's Avatar
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    U_5 + U_{16} = 44 and that  S_{18}=3*S_{10}

    Okay, 1st fact to remember
    An A.P. is of the form: a+(k-1)d, where k\geq1
    where U_k=a+(k-1)d and S_k=\frac{k(a+a+(k-1)d)}{2}

    so U_5=a+4d and U_{16}=a+15d
    and U_5+U_{16}=44
    2a+19d=44....(1)

    S_{18}=\frac{18(a+a+17d)}{2}
    S_{10}=\frac{10(a+a+9d)}{2}

    S_{18}=3*S_{10}
     \frac{18(a+a+17d)}{2}=3(\frac{10(a+a+9d)}{2})....(  2)

    Solve equations (1) and (2) simultaneously to obtain your answer.
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  3. #3
    cpj
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    Thanks!!
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