Question 1106609
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<U>Step 1</U>.  Divide both sides by {{{n/2}}}.   You will get   {{{S/((n/2))}}} = 2a + (n-1)*d,   or   {{{(2*S)/n}}} = 2a + (n-1)*d.    (1)


<U>Step 2</U>.  In (1),  subtract (n-1)*d from both sides.  You will get   2a = {{{(2S)/n}}} - {{{(n-1)*d}}}.                  (2)



<U>Step 3</U>.  In (2), divide both sides by 2 and get the   <U>ANSWER</U>   a = {{{S/n}}} - {{{((n-1)*d)/2}}}.
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