Question

Find the 7th term of the geometric sequence whose common ratio is 1/3 and whose first term is 5.

Answer 1

`t_7 =(5)/(729)`

Explanation:

We are given that:

First term (a) = 5

common ratio (r) =
`(1)/(3)`

The nth term of a geometric sequence is given as:

`t_n =ar^(n-1) \\\therefore t_7 =5* \bigg((1)/(3)\bigg) ^(7-1) \\\therefore t_7 =5* \bigg((1)/(3)\bigg) ^(6) \\\therefore t_7 =5* \bigg((1)/(3)\bigg) ^(6) \\\therefore t_7 =5* (1)/(729)\\\\\huge\red{\boxed{\therefore t_7 =(5)/(729) }}`