Question #1f6de

1 Answer
Feb 21, 2017

Answer:

#a_4=a_3xx6 " "=" " 144xx6 " "=" " 864#

#a_5=a_5xx6" "=" "864xx6" "=" "5184#

#a_6=a_5xx6" "=" "5184xx6" "=" " 31122#

Explanation:

Let the term count be #i#
Let the ith term be #a_i#

So we have:
#i=1->a_i =a_1=4#
#i=2->a_i=a_2=24#
#i=3->a_i=a_3=144#

The question states this is a geometric sequence.

Let the expression for the term be #a_ir^n#
Where #r# is the common ratio and #n# is some variant (function) of #i#

#color(brown)("Determine the value of "r)#

#24/4= 6#

#144/24=6#

Thus #r=6#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("Determine the next three terms")#

The last known term is #a_3=144#

so we have:

#a_4=a_3xx6 " "=" " 144xx6 " "=" " 864#

#a_5=a_5xx6" "=" "864xx6" "=" "5184#

#a_6=a_5xx6" "=" "5184xx6" "=" " 31122#