SOLUTION: The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set? (A) 25 (B) 26 (C) 50 (D) 51 (E) 52

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set? (A) 25 (B) 26 (C) 50 (D) 51 (E) 52       Log On


   



Question 303188: The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set?
(A) 25 (B) 26 (C) 50 (D) 51 (E) 52

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
The least integer of a set of consecutive integers is -25. If the sum of these integers is 26, how many integers are in this set?
(A) 25 (B) 26 (C) 50 (D) 51 (E) 52
1/2 * n(n+1) = 1/2 * 25 * 26 = 325
the sum of the 25 negative integers is the same as the sum of the 25 positive integers multiplied by -1 so that adds up to 0, the 51st integer is 0 itself, the 52nd integer is 26
(E) 52