Writing x = ar³, y = ar⁹ and z = ar¹⁵, we compute y² = (ar⁹)² = a²r¹⁸. Also x x z = (ar³) x (ar¹⁵) = a²r¹⁸. Since y² = x x z, x, y, z form a GP.
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Writing x = ar³, y = ar⁹ and z = ar¹⁵, we compute y² = (ar⁹)² = a²r¹⁸. Also x x z = (ar³) x (ar¹⁵) = a²r¹⁸. Since y² = x x z, x, y, z form a GP.