Find a Formula for the Sum and Then Use It $$\sum _ { k = 1 } ^ { n } ( 2 - k )$$

Multiple Choice

Find a formula for the sum and then use it to calculate the sum for n = 100, n = 500, and n = 1000. $$\sum _ { k = 1 } ^ { n } ( 2 - k )$$

A) $\frac { 3 n + n ^ { 2 } } { 2 }$
B) $\frac { 4 n - n ^ { 2 } } { 2 }$
C) $\frac { 3 n - n ^ { 2 } } { 2 }$
D) $\frac { 2 n - n ^ { 2 } } { 2 }$