Sequencce (Xn) please?

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1 Answer
Jun 1, 2018

Answer:

See process below

Explanation:

Take a look to the first four terms

#6.5, -27.3, 114.66, -481.572,....#

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

#-27.3/6.5=-21/5#
#114.66/-27.3=-21/5# and so on...

Then the comon ratio is #r=-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=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)