Question

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

Answer 1

Answer:

a = 12 and b = 18

Step-by-step 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

$a_4=ar^{4-1}\\\\a_4=ar^3\\\\27=8\times r^3\\\\r^3=\dfrac{27}{8}\\\\r=\dfrac{3}{2}=1.5$

Put n = 2,

$a_2=ar^{2-1}\\\\a=ar\\\\a=8\times 1.5\\\\a=12$

Put n = 3

$a_3=ar^2\\\\=8\times 1.5^2\\\\b =18$

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