Question 1086032
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<pre>
{{{a[3]}}} = {{{a[1]*r^2}}} = 3,     (1)

{{{a[6]}}} = {{{a[1]*r^5}}} = {{{1/9}}}.     (2)


Divide eq(2) by eq(1) (both sides). You will get 

{{{a[6]/a[3]}}} = {{{r^5/r^2}}} = {{{r^3}}} = {{{((1/9))/3}}} = {{{1/27}}},

which implies  

r = {{{1/3}}}.


Thus we found the common ratio. It is r = {{{1/3}}}.


Then from  (1)  {{{a[1]}}} = {{{3/r^2}}} = {{{3/((1/9))}}} = 27.


The progression is 27, 9, 3, 1, {{{1/3}}}, {{{1/9}}}.
</pre>

<U>Answer</U>.  {{{a[1]}}} = 27.


Solved.