Question 1135842
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<pre>
Let x be the middle term {{{a[2]}}}.  

Then  {{{a[1]}}} = x - d,  {{{a[3]}}} = x + d.


Also,  {{{a[1]}}} + {{{a[2]}}} + {{{a[3]}}} = (x-d) + x + (x+d) = 3x,  


therefore the first statement of the condition means that


    3x = 21,  which  implies  x = {{{a[2]}}} = 21/3 = 7.


The second statement of the condition means then that

    {{{a[1]}}}.{{{a[3]}}} = (7-d)*(7+d) = 7 + 6 = 13,   or

    {{{49 - d^2}}} = 13  ====>  {{{d^2}}} = 49 - 13 = 36  ====>  d = {{{sqrt(36)}}} = +/- 6.


So, the three terms of the progression are EITHER

    7 - 6 = 1, 7, 7 + 6 = 13


OR in reverse order

    13, 7, 1.
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Solved.