Mathematics

A GP is such that the 3rd term is nine times the 1st term while the 2nd term is one - twenty fourth of the 5th term .Find it's fourth term.

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  1. This cannot be solved because:

    In GP:

    an = a1 ∙ r ⁿ ⁻ ¹

    a2 = a1 ∙ r

    a3 = a1 ∙ r²

    a5 = a1 ∙ r⁴

    a3 = 9 a1

    a1 ∙ r² = 9 a1

    Divide both sides by a1

    r² = 9

    r = ± √ 9

    r = ± 3

    a2 = a5 / 24

    a1 ∙ r = a1 ∙ r⁴ / 24

    Divide both sides by a1 ∙ r

    1 = r³ / 24

    Multiply both sides by 24

    24 = r³

    The result is:

    24 = r³

    24 = ( - 3 )³ = - 27

    OR

    24 = 3³ = 27

    That is obviously not true.

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