SOLUTION: The sum S of a list of consecutive integers beginning with one can be determined by evaluating the formula S=n/2(n+1), where n is the number of integers in the list. Using this fo

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The sum S of a list of consecutive integers beginning with one can be determined by evaluating the formula S=n/2(n+1), where n is the number of integers in the list. Using this fo      Log On


   

Question 295510: The sum S of a list of consecutive integers beginning with one can be determined by evaluating the formula S=n/2(n+1), where n is the number of integers in the list. Using this formula, determine the number of consecutive positive integers beginning with one that must be added together so that the sum is 703.
Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
S+=+n%2F2+%2A+%28n+%2B+1%29
703+=+n%2F2+%2A+%28n+%2B+1%29
703+=+n%5E2%2F2+%2B+n%2F2%29
multiply all by 2
1406+=+n%5E2+%2B+n%29
0+=+n%5E2+%2B+n+-+1406%29
0+=+%28n+-+37%29%2A%28n+%2B+38%29
n - 37 = 0 or n + 38 = 0
n = 37 or n = -38
because the number of the integers can't be a negative number, so the number of the integers = 37