The sum of the first 150 negative integers is represented using the expression What is the sum of the first 150 negative integers? A. –22,650 B. –22,350 C. –11,325 D. –11,175

Answer:C. -11,325Step-by-step explanation:To know the answer, is convenient to replace some values of "n" in the sum [tex]\sum_{(n=1)}^{150}[-1-(n-1)][/tex].The result would appear after adding up every value of the expression [tex]\sum_{(n=1)}^{150}[-1-(n-1)][/tex] when n=1,2,3.....,150.When n=1, the expression takes the value of (-1): [tex][-1-(1-1)]= (-1)-0=-1[/tex].When n=2, the expression takes the value of (-2): [tex][-1-(2-1)]=-1-1=-2[/tex].Following this way, for every n, we will obtain -n, then, the sum will be: [tex]-1-2-3-4-5-6-...-150[/tex]. This sum can actually be expressed as [tex]\sum_{n=1}^{150}(-n)[/tex], which is the result of solving the initial expression of the sum [tex]-1-(n-1)=-1-n+1=-n[/tex].Finally, the sum of n=-1 to n=-150 equals -11,325.