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the 3rd term of a g.p is 63 while the 5th term is 567,what is the sum of the first 7 terms

  • maths -

    t(5) = ar^4 = 567
    t(3) = ar^2 = 63

    divide first equation by the second

    ar^4/(ar^2) = 567/63
    r^2 = 9
    r = ± 3

    if r = ±3,
    ar^2= 63
    a = 7

    Since you only want 7 terms, it would probably be faster to just find them and add them up

    that is,
    7 + 21 + 63 + 189 + 567 + 1701 + 5103 = 7651

    or 7 - 21 + 63 - 189 + 567 - 1701 - 5103 = ......

    or by formula
    if a=7, r= 3
    sum(7) = 7(3^7 - 1)/(3-1) = 7651

    or if x=-3
    sum(7) = 7((-3)^7 - 1)/(-3-1) = .....

  • maths -

    The third term of a g p is 63 while the 5th term is 567 what is the sum of the first seven terms

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