The sum of the first 50 positive odd integers is $50^{2}$. The sum of the first 50 positive even integers is
(A) $50^{2}$
(B) $50^{2}+1$
(C) $50^{2}+25$
(D) $50^{2}+50$
(E) $50^{2}+100$
Solution

An even integer is found by taking the previous odd integer and adding 1.

Thus, the sum of the first 50 positive even numbers is obtained by finding the sum of the first 50 positive odd integers then adding 501 's.

The sum of the first 50 positive even integers is $50^{2}+50$.

ANSWER: (D)

#