Question

If 8,a,b,27 are in geometric sequence, find the value of a and b.​

Answer 1

a = 12 and b = 18

Explanation:

Given that,

8,a,b,27 are in geometric sequence.

For a GP, the nth term is given by :

`a_n=ar^(n-1)`

Put n = 4

`a_4=ar^(4-1)\\\\a_4=ar^3\\\\27=8* r^3\\\\r^3=(27)/(8)\\\\r=(3)/(2)=1.5`

Put n = 2,

`a_2=ar^(2-1)\\\\a=ar\\\\a=8* 1.5\\\\a=12`

Put n = 3

`a_3=ar^2\\\\=8* 1.5^2\\\\b =18`

So, the values of a and b is 12 and 18 respectively.