Jun 1, 2018

See process below

#### Explanation:

Take a look to the first four terms

$6.5 , - 27.3 , 114.66 , - 481.572 , \ldots .$

First: we note that terms are alternate positive and negative, so the ratio is a negative number. Lets see

$- \frac{27.3}{6.5} = - \frac{21}{5}$
$\frac{114.66}{-} 27.3 = - \frac{21}{5}$ and so on...

Then the comon ratio is $r = - \frac{21}{5}$

a) The recurrence system is a_n=a_(n-1)·(-21/5)

By other hand, we know that a geometric sequence has the general term given by

a_n=a_1·r^(n-1) where ${a}_{0}$ is the first term ${a}_{1} = 6.5 = \frac{13}{2}$

Then a_n=13/2·(-21/5)^(n-1) This is the answer for b)

c) a_8=13/2·(-21/5)^7=6.5xx-23053.93332=-149850.5666

d) However the common ratio is bigger than 1, when n increase his value, the terms grow indefinitely alternating sign (the even terms are negatives and odd positives)