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:

$\dfrac{80}{16}=5$

$\dfrac{400}{80}=5$

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.