Find the product xy if, x, 3/2, 6/7, y are in G.P

In GP, when you are given three consecutive terms, say f, g, h, then

\(f \times h = g^2\)

Given: \(x, \frac{3}{2}, \frac{6}{7}, y\), then

\(\frac{6x}{7} = (\frac{3}{2})^2 \implies \frac{6x}{7} = \frac{9}{4} ... (i)\)

Also, \(\frac{3y}{2} = (\frac{6}{7})^2 \implies \frac{3y}{2} = \frac{36}{49} ... (ii)\)

From \(\frac{6x}{7} = \frac{9}{4} \implies x = \frac{9 \times 7}{6 \times 4}\)

\(x = \frac{21}{8}\)

Also, \(\frac{3y}{2} = \frac{36}{49} \implies y = \frac{2 \times 36}{3 \times 49}\)

= \(\frac{24}{49}\)

\(xy = \frac{21}{8} \times \frac{24}{49} = \frac{9}{7}\)

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