1985 AJHSME Problems/Problem 2
Problem
Solution
Solution 1
One possibility is to simply add them. However, this can be time-consuming, and there are other ways to solve this problem. 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 (First term+Last term) where is the number of terms in the sequence.
Applying it here:
See Also
1985 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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