Question

the 6th , 9th , 12th terms of Geometric progression is a, b and c , then show b^2 = ac​

Answer 1

Step-by-step explanation:

Let the first term be 'a' and common ratio be 'r'.

nth term = ar^(n-1), so,

6th term = ar^(6-1) = ar^5, similarly,

9th term = ar^8

12th term = ar^11

Solving LHS: b^2 = (ar^8)^2 = a^2 x r^16

RHS: ac =(ar^5).(ar^11) = a^2 x r^16

Notice that LHS = RHS, as desired.