Question

The sum of the first 150 negative integers is represented using the expression

Answer 1

C.)

Explanation:

Answer 2

`\large\boxed{-11,325}`

Explanation:

First simplify:

`-1-(n-1)=-1-n-(-1)=-1-n+1=-n`

Therefore we have:

`\sum\limits_(n=1)^(150)[-1-(n-1)]=\sum\limits_(n=1)^(150)(-n)=(-1)+(-2)+(-3)+...+(-150)\\\\-1,\ -2,\ -3,\ -4,\ ...,\ -150-\text{it's the arithmetic sequence}\\\text{with the common difference d = -1.}\\\\\text{The formula of a sum of terms of an arithmetic sequence:}\\\\S_n=(a_1+a_n)/(2)\cdot n\\\\\text{Substitute}\ n=150,\ a_1=-1,\ a_n=-150:\\\\S_(150)=(-1+(-150))/(2)\cdot150=(-151)(75)=-11,325`