Question

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

16, 80,400,...
16,80,400,...
\text{Find the 6th term.}
Find the 6th term.

Answer 1

Given:

The sequence is:

`16,80,400,...`

To find:

The 6th term of the given sequence.

Solution:

We have,

`16,80,400,...`

Here, the first term is:

`a=16`

The ratio between consecutive terms are:

`(80)/(16)=5`

`(400)/(80)=5`

The given sequence has a common ratio 5. So, the given sequence is a geometric sequence.

The nth term of a geometric sequence is:

`a_n=a(r)^(n-1)`

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

Substitute
`a=16,r=5,n=6` to get the 6th term.

`a_6=16(5)^(6-1)`

`a_6=16(5)^(5)`

`a_6=16(3125)`

`a_6=50000`

Therefore, the 6th term of the given sequence is 50000.