Question

What is the 9th term of the following geometric sequence? 7/9,-7/3,7,-21,63 ??????

Answer 1

Given:

The geometric sequence is:

`(7)/(9),(-7)/(3),7,-21,63,...`

To find:

The 9th term of the given geometric sequence.

Solution:

We have,

`(7)/(9),(-7)/(3),7,-21,63,...`

Here, the first term is:

`a=(7)/(9)`

The common ratio is:

`r=(a_2)/(a_1)`

`r=((-7)/(3))/((7)/(9))`

`r=(-7)/(3)* (9)/(7)`

`r=-3`

The nth term of a geometric sequence is:

`a_n=ar^(n-1)`

Where, a is the first term and r is the common ratio.

Substitute
`a=(7)/(9),r=-3,n=9` to find the 9th term.

`a_9=(7)/(9)(-3)^(9-1)`

`a_9=(7)/(9)(-3)^(8)`

`a_9=(7)/(9)(6561)`

`a_9=5103`

Therefore, the 9th term of the given geometric sequence is 5103.