Question 803100
<pre>
360,180,120,90,<u> x </u>,<u> y </u>

{{{180/360}}} equals to {{{1/2}}}
{{{120/180}}} equals to {{{2/3}}}
{{{90/120}}} equals to {{{3/4}}}
So inductively,
{{{x/90}}} must equal to {{{4/5}}}
 {{{x/90}}}{{{""=""}}}{{{4/5}}}
5x = 360
 x = 72
Also inductively,
{{{y/x}}} or {{{y/72}}} must equal to {{{5/6}}}
      {{{y/72}}}{{{""=""}}}{{{5/6}}}
     6y = 360
      y = 60

360,180,120,90,<u> 72 </u>,<u> 60 </u>.

-------------------------------------

 1,5,14,30,55,<u> x </u>,<u> y </u>

  5-1 equals to 4, which equals to 2².
 14-5 equals to 9, which equals to 3².
30-14 equals to 16, which equals to 4².
55-30 equals to 25, which equals to 5².

So inductively,
x-55 must equal to 6² or 36
x-55 = 36
   x = 91
 
Also inductively,
y-x or y-91 must equal to 7² or 49
       y-91 = 49
          y = 140

 1,5,14,30,55,<u> 91 </u>,<u> 140 </u>.

Edwin</pre>