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Answer 1 · 2017-02-21T11:34:42

$a_4=a_3xx6 " "=" " 144xx6 " "=" " 864$

$a_5=a_5xx6" "=" "864xx6" "=" "5184$

$a_6=a_5xx6" "=" "5184xx6" "=" " 31122$

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:

$a_4=a_3xx6 " "=" " 144xx6 " "=" " 864$

$a_5=a_5xx6" "=" "864xx6" "=" "5184$

$a_6=a_5xx6" "=" "5184xx6" "=" " 31122$