Question

Insert 3 geometric means between 1/9 and 9​

Answer 1

Answer:

1.1/9 < 9

2.1 part is 9 times, 9is 9parts

Answer 2

Here,

First term (a) = 1/9

Last term (b) = 9

No. of means (n) = 3

Now,

Common ratio (r) = $(b/a)^{1/n+1}$

=$(9/(1/9))^{1/3+1}$

=$(81)^{1/4}$

=$(3)^{4*\frac{1}{4} }$

=3

Lastly,

First mean = ar =1/9*3 =1/3

Second mean = a$r^{2}$ =1/9*9 = 1

Third mean =a$r^{3}$ = 1/9*27 = 3

Hence, the three G.M. are (1/3 , 1 , 3).

Hope its helpful.