math help!

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the 10th term is 34 of arithmetic series and the sum of the 20th term is 710 i.e S20=710.what is the 25th term?

  • math help! -

    Let a = first term, T1
    Let b = Tn+1 - Tn = term difference

    a + 9b = 34
    S20 = T1 + T2 + ...T19 + T20
    = a + (a+b) + (a+2b) + ...(1+19b)
    20a + (b)(1+2+3+...19)
    = 20 a + 190 b = 710

    20a + 180b = 680
    10 b = 30
    b = 3
    a = 34 -27 = 7

    Arithmetic Series is
    7, 10, 13, 16, 19, 22, 25, 28, 31, 34,...
    10th term = 34

    Check the sum of the first 20 terms and predict the 25th

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