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An arithmetic and a geometric sequence have the same first terms.(2)....and the same second term say X..The sum of the first 3 terms of the arithmetic sequence equals to the third term of the geometric sequence.Calculate the first 3 terms of each sequences

  • Maths -

    a+d = ar
    3/2 (2a+2d) = ar^2
    3a+3d = ar^2
    3(a+d) = ar^2
    3ar = ar^2
    3r = r^2
    r = 3

    So,
    a+d = 3a
    d = 2a

    The sequences are thus
    a,3a,5a,7a,9a,...
    a,3a,9a,27a,...
    Note that a+3a+5a = 9a, as required

    Pick a value for a, and plug and chug.

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