Question 1135894
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  {{{a[1]}}} + {{{a[2]}}} + {{{a[3]}}} + {{{a[4]}}} + {{{a[5]}}} + {{{a[6]}}} = 


= {{{a + ar + ar^2 + ar^3 + ar^4 + ar^5}}} = {{{(a + ar + ar^2)}}} + {{{r^3*(a+ar + ar^2)}}} = {{{(1 + r^3)*(a + ar + ar^2)}}}.


Therefore,


{{{(a+ar + ar^2)/(a + ar + ar^2 + ar^3 + ar^4 + ar^5)}}} = {{{1/(1 + r^3)}}} = {{{27/19}}}.


Hence,   {{{1 + r^3}}} = {{{19/27}}}   and  {{{r^3}}} = {{{19/27 - 1}}} = {{{8/27}}}.


It implies   r = {{{root(3,8/27)}}} = {{{2/3}}}.


<U>Answer</U>.  r = {{{2/3}}},  which is the  first line of the option's list.
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