Question 1167377
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Then the term  {{{1/x}}}  is the arithmetic mean of its neighbors


    {{{1/x}}} = {{{(1+2)/2}}} = {{{3/2}}},   so  x = {{{2/3}}}.



Hence, the terms  {{{3/2}}}, 2 and y form a geometric progression.


Then the ratio of this progression is  {{{2/((3/2))}}} = {{{4/3}}}  and  y = {{{2*(4/3)}}} = {{{8/3}}}.


<U>ANSWER</U>.  x= {{{2/3}}},  y= {{{8/3}}}.
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Solved.