Question 836400
{{{a[1]=1}}} {{{a[4]=27}}}
 
In a geometric sequence,
{{{r}}}= common ratio
{{{a[n]=a[1]*r^(n-1)}}} for any natural number {{{n}}}
 
{{{1*r^(4-1)=27}}}
{{{r^3=27}}} so {{{highlight(r=3)}}}
(You must know that {{{3^3=3*3*3=9*3=27}}} so you know where I got that {{{r}}} value).
{{{a[7]=1*3^(7-1)}}}
{{{a[7]=3^6}}}
 
You see that choices A and D are not even multiples of 3, so they are not the answer.
(If they were multiples of 3, their digits would add up to 3, 6, 9, or some other multiple of 3).

{{{3^6=3^(3*2)=(3^3)^2=27^2}}}
I see immediately that B and C are also wrong, because the answer should be between 625 and 900:
{{{25<27<30}}} <--> {{{625=25^2<27^2<30^2=900}}}
It may be a typo (not necessarily your fault), or else someone is making a mistake in the calculations (and I say not me). 

However,
{{{2187=3^7}}} and {{{1953=3^2*7*31}}}
I would choose answer {{{highlight("B . 2187")}}}
and use judgement about confronting the teacher, or textbook maker about their mistake. If you already had the test, make sure you did not misread the question, and if the question was wrong, meekly point out that you knew the right answer, but were confused and frustrated by the choices given. Maybe you can gain more points that way.