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 11492 views around the world You can reuse this answer Creative Commons License