Insert two numbers between \( 3 \) and \( 81 \) so that the resulting sequence is a G.P.

Let the two numbers be \( G_1, G_2 \) making a 4-term G.P: \( 3, G_1, G_2, 81 \). Here \( a = 3, ar^3 = 81 \implies r^3 = 27 \implies r = 3 \). Thus \( G_1 = 3 \times 3 = 9 \) and \( G_2 = 9 \times 3 = 27 \).