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\(U_1 = a = 32\)

\(U_4 = ar^3 = 621\)

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)

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