How do you solve for n in S = (n(n+1))/ 2? Algebra Linear Equations Multi-Step Equations with Like Terms 1 Answer Himanshu Shekhar Jun 7, 2016 n = (-1 +- sqrt(1+8S))/(2) Explanation: S = (n(n+1))/2 S = (n^2+n)/2 2S = n^2 +n n^2 + n - 2S = 0 using the quadratic formula for : ax^2 + bx + c = 0, n = (-b +- sqrt( b^2 - 4ac) ) /(2a) n = (-1 +- sqrt(1 - 4(1)(-2S)))/2 n = (-1 +- sqrt(1+8S))/(2) Answer link Related questions How do you solve multi step equations by combining like terms? How do you solve multi step equation w + w + 12 = 40? How do you solve 3p + 4p + 37 = 79? How do you solve for f: f-1+2f+f-3=-4? How do you combine like terms? How do you combine like terms for -7mn-2mn^2-2mn + 8? How do you combine like terms for 3x^2 + 21x + 5x + 10x^2? What is a term? How do you solve 3v+5-7v+18=17? How do you solve for x in 5x + 7x = 72? See all questions in Multi-Step Equations with Like Terms Impact of this question 11750 views around the world You can reuse this answer Creative Commons License