Question

Find three numbers in GP. Whose sum is 35 and sum of whose squares is 525.

Answer 1

Let the three numbers be a, ar, ar2 which are is GP.

Given a + ar + ar2 = 35 ⇒ a( 1 + r + r2) = 35

and a2 + a2 r2 + a2 r4 = 525

⇒ a2(1 + r2 + r4) = 525

when r = -2 2ar = -20 ⇒ -4a = -20 [∴ a = 5]

when r = -1/2, 2ar = -20 ⇒ -a = -20 ⇒ [a = 20]

Hence the three number which are in G.P are 5, -10, 20 (or) 20, – 10, 5