Question

# The sum of three numbers in G.P. is 21 and the sum of their squares is 189. Find the numbers.

Let three numbers in G.P. be a, ar, ar2
Since the sum of the numbers is 21

∴                     a + ar + ar2 = 21                                   ...(i)
Since the sum of the squares of the numbers is 189
∴                                   ...(ii)
Squaring both sides of (i), we get
...(iii)
Dividing (iii) by (ii), we get

When r = 2, from (i),
a = 3
∴     Numbers are 3, 3(2), 3(2)2  or 3, 6, 12
When     from (i),
a = 12
∴ Numbers are 12,    or 12, 6, 3