2008 AIME II Problems/Problem 6
Problem
The sequence is defined by The sequence is defined by Find .
Solution
Rearranging the definitions, we have from which it follows that and . These recursions, and , respectively, correspond to the explicit functions and (after applying our initial conditions). It follows that .
From this, we can determine that the sequence corresponds to the triangular numbers.
See also
2008 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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All AIME Problems and Solutions |