Answer
please see step-by-step
Work Step by Step
(see p. 858)
A geometric sequence is a sequence whose terms are obtained by multiplying each term by the same fixed constant $r$ to get the next term.
A geometric sequence has the form $a, ar, ar^{2}, ar^{3}, \ldots$
The number $a$ is the first term of the sequence,
and the number $r $is the common ratio.
The nth term of the sequence is $\quad a_{n}=ar^{n-1}$
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$a_{1}=a=3$
$a_{2}=3(2i)=6i$,
$a_{3}=6i(2i)=3(2i)^{2}=3(-4)=-12$
$a_{4}=-12(2i)=3(2i)^{2}(2i)=3(2i)^{3}=3(-8i)=-24i$
$...$
$a_{n}=3(2i)^{n-1}$
$3,\ 6i, -12, -24i,\ \ldots$.
is a geometric sequence with
$a=3,$
common ratio $r=2i$.
