Select the Right Expression for the Following Sum and Prove $$P _ { \mathrm { n } } : 8 + 6 + 4 \ldots ( 10 - 2 n )$$

Multiple Choice

Select the right expression for the following sum and prove that your statement is true for all natural numbers n. $$P _ { \mathrm { n } } : 8 + 6 + 4 \ldots ( 10 - 2 n )$$

A) $\quad 9 n - n ^ { 2 }$
B) $\quad 9 n - 2 n ^ { 2 }$
C) $\quad 11 n - 2 n ^ { 2 }$
D) $\quad 11 n - n ^ { 2 }$
E) none of the above