Question

The sum of three numbers in G.P. is 70. If the two extremes by multiplied each by 4 and the mean by

5, the products are in AP. The numbers are
(a) 12, 18, 40

(b) 10, 20, 40

(c) 40, 20, 15

(d) none of these​

Answer 1

Answer:

Let a,ar,ar^2 be three terms of G.P.

Common ratio =r

Given :

a+ar+ar^2 =70 .......... (1)

Also, 4a,5ar,4ar^2 are in A.P.

∴4a+4ar^2 =2×5ar

⇒2+2r^2=5

⇒2r^2−5r+2=0

∴r=2, 1/2

Putting value of r=2 in eqn. (1), we get

a(1+2+4)=70

⇒a=10

Thus, the numbers are 10,20,40.

hope you understand