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Insert two geometric means between 32 and 62


Question

Insert two geometric means between 32 and 62

Options

A) (16, 32)

B) (40, 50)

C) (44.72, 52.87)

D) (47.25, 54.88)

The correct answer is B.

Explanation:

\(U_1 = a = 32\)
\(U_4 = ar^3 = 621\)
Assuming \(x\) and \(y\) are the geometric means
\(\cfrac{U_4}{U_1} =\cfrac{ar^3}{a} = \cfrac{125}{2 \times 32} = \cfrac{125}{64}\)
\(r^3 = \cfrac{125}{64}\)
\(r = \sqrt[3]{\cfrac{125}{64}} = \cfrac{5}{4}\)
\(x = U_2 = ar = 32(\cfrac{5}{4}) = 40\)
\(y = U_3 = ar^2 = U_2 \times r = 40 \times \cfrac{5}{4} = 50\)
The geometric means are (40, 50)

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Discussion (2)

  • \(U_1 = a = 32\)
    \(U_4 = ar^3 = 621\)
    Assuming \(x\) and \(y\) are the geometric means
    \(\cfrac{U_4}{U_1} =\cfrac{ar^3}{a} = \cfrac{125}{2 \times 32} = \cfrac{125}{64}\)
    \(r^3 = \cfrac{125}{64}\)
    \(r = \sqrt[3]{\cfrac{125}{64}} = \cfrac{5}{4}\)
    \(x = U_2 = ar = 32(\cfrac{5}{4}) = 40\)
    \(y = U_3 = ar^2 = U_2 \times r = 40 \times \cfrac{5}{4} = 50\)
    The geometric means are (40, 50)

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    1. Please can you explain why Ur³ became 125 and not 621 and why did you times 32 by 2?

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