Question 340360: If the sum of the consecutive integers from -22 to x, inclusive, is 72, what is the value of x?
A. 23 B. 25 C. 50 D. 75 E. 94
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! If the sum of the consecutive integers from -22 to x, inclusive, is 72, what is the value of x?
A. 23 B. 25 C. 50 D. 75 E. 94
sum -1 to -22 --> same as sum of 1 to 22 but multiply result by -1
sum 1 to 22 = 1/2 * n * (n + 1) = 1/2 * 22 * 23 = 506/2 = 253
sum -1 to -22 = -253
so sum -22 to 22 = 0
what range of positive integers adds to 253 + 72 = 325 ?
1/2 * n * (n + 1) = 325
1/2 * (n^2 + n) = 325
n^2 + n = 650 (multiplied both sides by 2)
n^2 + n - 650 = 0
factor 650:
650 = 10 * 65 = 10 * 13 * 5 = 2 * 5 * 5 * 13 = 25 * 26
check factors:
(n - 25)(n + 26) --> FOIL (First Inner Outer Last) --> n^2 + 26n - 25n - 650
n = 25 or n = -26, throw negative result out
so:
1 to 25 adds to 325
answer is B. 25
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