SOLUTION: Make a the subject of the formule in the equation s=n\2[2a+(n-1)d]

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Question 1180654: Make a the subject of the formule in the equation s=n\2[2a+(n-1)d]
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
s=n\2[2a+(n-1)d]
2s/n = 2a+(n-1)d
(2s/n)/(n-1)d =2a
%282s%2Fn%29%2F%28%28n-1%29d%2A2%29+=a

%282s%29%2F%28%28n-1%29d%2A2n%29+=a





Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
Make a the subject of the formula in the equation s = (n/2)*(2a+(n-1)d).
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            Please pay attention how I edited your writing to make the formula correct. 


You start from

    s = %28n%2F2%29%2A%282a%2B%28n-1%29d%29.



Multiply both sides by  %282%2Fn%29.  You get then

    %282s%2Fn%29 = 2a + (n-1)d.



Next move the term (n-1)*d from the right side to the left side CHANGING ITS SIGN.  You will get then

    %282s%2Fn%29+-+%28n-1%29d = 2a.



Last step multiply both sides by  1%2F2.   You finally get

  
     +---------------------------------------+
     |   a = %281%2F2%29%2A%28%282s%2Fn%29+-+%28n-1%29d%29.          |
     +---------------------------------------+


It is your answer.


You can transform this final formula further as you wish (using equivalent transformations, ONLY).

Solved and carefully explained.


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Ignore the post by @mananth, since it is TOTALLY WRONG.