1985 AJHSME Problems/Problem 2
Problem
Solution
Solution 1
We could just add them all together. But what would be the point of doing that? So we find a slicker way.
We find a simpler problem in this problem, and simplify ->
We know , that's easy - . So how do we find ?
We rearrange the numbers to make . You might have noticed that each of the terms we put next to each other add up to 10, which makes for easy adding. . Adding that on to 900 makes 945.
945 is
Solution 2
Instead of breaking the sum and then rearranging, we can start by rearranging:
Solution 3
We can use a formula. It is n/2*(First term+Last term). Applying it here:
See Also
1985 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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