Question

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

Answer 1

Answer:

The 9th term for given sequence is 16.777

Therefore the 9th term is $a_{9}=16.777$.

Step-by-step explanation:

Given first three terms of a sequence are 100,80,64,...

Given $a_{1}=100$ ,$a_{2}=80$ , $a_{3}=64$,...

Given sequence is of the form of Geometric sequence

Therefore it can be written as ${\{a,ar,ar^2,...}\}$

therefore a=100 , ar=80 , $ar^2=64$ ,...

To find common ratio

$r=\frac{a_{2}}{a_{1}}$

$r=\frac{80}{100}$

$r=\frac{4}{5}$

$r=\frac{a_{3}}{a_{2}}$

$r=\frac{64}{80}$

$r=\frac{4}{5}$

Therefore $r=\frac{4}{5}$

The nth term of the geometric sequence is

$a_{n}=ar^{n-1}$

To find the 9th tem for the given geometric sequence is

$a_{n}=ar^{n-1}$

put n=9, a=100 and  $r=\frac{4}{5}$

$a_{9}=100(\frac{4}{5})^{9-1}$

$=100(\frac{4}{5})^{8}$

$=100(\frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5}\times \frac{4}{5})$

$=100(\frac{256\times 256}{625\times 625})$

$=100(\frac{65536}{390625})$

$=100(0.16777})$

$=16.777$

Therefore $a_{9}=16.777$

The 9th term is 16.777