Question

The first three terms of a sequence are given. Round to the nearest thousandth ( if necessary)

12, 36, 108

Find the 9th term

Answer 1

a₉ = 78732

Explanation:

there is a common ratio between consecutive terms , that is

`(36)/(12 )` =
`(108)/(36)` = 3

this indicates the sequence is geometric with nth term

`a_(n)` = a₁
`r^(n-1)`

where a₁ is the first term and r the common ratio

here a₁ = 12 and r = 3 , then

a₉ = 12 ×
`3^(8)` = 12 × 6561 = 78732