1993 UNCO Math Contest II Problems/Problem 5
Problem
A collection of consecutive positive integers adds to What are the smallest and largest integers in this collection?
Solution
Solution 1
The thirteenth integer is the average, which is . So, the largest integer is 12 larger, which is , and the smallest integer is 12 less, which is .
Solution 2
By the summation formula, the sum of 25 consecutive numbers (where is the smallest number in the list) is Letting the value of the equation be , we have Thus the smallest value of the list is , and the largest is
See also
1993 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |