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10 June, 08:41

Find two geometric means between 5 and 135

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  1. 10 June, 09:00
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    We are effectively looking for a and b such that 5, a, b, 135 is a geometric sequence.

    This sequence has common ratio 3 √ 1355 = 3, hence a=15 and b=45

    Explanation:

    In a geometric sequence, each intermediate term is the geometric mean of the term before it and the term after it.

    So we want to find a and b such that 5, a, b, 135 is a geometric sequence.

    If the common ratio is r then:

    a=5r b=ar=5 r2 135=br=5 r3

    Hence r3 = 1355 = 27, so r = 3 √27 = 3

    Then a=5r=15 and b=ar=15⋅3=45
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