SOLUTION: Make n the subject formula in s=n/2[2a+(n-1)d]

Clear the fraction by multiplying both sides by 2:



Swap the d and the (n-1)



Remove the inner parentheses on the right by distributing:



Remove the remaining parentheses on the right by distributing:



Get 0 on the left by subtracting 2s from both sides:



Swap sides:



Rearrange the terms in descending order



Factor n out of the two terms in the middle:



Swap the n and the (2a-d)



We use the quadratic formula.  Since there is 
already a letter "a", we will use capital letters
to avoid conflict of notation:

Ax2 + Bx + C = 0 has solution



x = n, A = d, B = (2a-d), C = -2s





Edwin