Question

What is the 6th term of the geometric progression
12.6.3, ... ?

Answer 1

a₆ =
`(3)/(8)`

Explanation:

The n th term of a geometric progression is

`a_(n)` = a₁
`r^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = 12 and r =
`(a_(2) )/(a_(1) )` =
`(6)/(12)` =
`(1)/(2)` , thus

a₆ = 12
`((1)/(2)) ^(5)` = 12 ×
`(1)/(32)` =
`(12)/(32)` =
`(3)/(8)`