Question

The sum of three numbers in G.P. is 70. If the two extreme terms are each multiplied by 4 and the geometric mean of these three terms is multiplied by 5, the first term multiplied by 4, the geometric mean and the third term multiplied by 4are in A.P. the numbers are:​

Answer 1

$\huge\fcolorbox {magenta} {red} {Answer}$

Let a,ar,ar² be three terms of G.P.

Common Ratio = r

Given :

a+ar+ar²=70

Also, 4a,5ar,4ar² are in A.P.

4a+4ar²=2×5ar

2+2r²=5r

2r²-5r+2=0

r = 2,1/2

a(1+2+4)=70

a = 10

Thus the number are 10,20,40