Question

insert 5 geometric means between 4/5 and 5/6.​

Answer 1

Answer:

Let a1 , a2 , a3 , a4 , a5 be 5 gepmetric means between a = 576 and b = 9

So, the sequence a, a1 , a2 , a3 , a4 , a5 , b is in GP

Now, common ratio r = (b/a)1/(n + 1)

=> r = (9/576)1/(5 + 1)

=> r = (1/64)1/6

=> r = (1/26 )1/6

=> r = 1/2

Now, a1 = ar = 576 * (1/2) = 576/2 = 288

a2 = ar2 = 576 * (1/2)2 = 576/4 = 144

a3 = ar3 = 576 * (1/2)3 = 576/8 = 72

a4 = ar4 = 576 * (1/2)4 = 576/16 = 36

a5 = ar5 = 576 * (1/2)5 = 576/32 = 18

So, 288, 144, 72, 36, 18 are the 5 geometric means inserted between 576 and 9