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WAEC 2025

If \(\frac{16}{9}\), x, 1, y are in geometric progression (G.P.). Find the product of x and y.

  1. A\(\frac{16}{9}\)
  2. B\(\frac{3}{4}\)
  3. C1
  4. D\(\frac{4}{3}\)

Explanation

In a G.P., the nth term is T_n = a*r^(n-1). Given T_1 = 16/9 and T_3 = 1, we have a = 16/9 and a*r^2 = 1, which gives r^2 = 9/16. Since x = T_2 = a*r and y = T_4 = a*r^3, the product x*y = (a*r)*(a*r^3) = a^2*r^4 = (a*r^2)^2 = 1^2 = 1.

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