1992 AIME Problems/Problem 8
Contents
[hide]Problem
For any sequence of real numbers , define to be the sequence , whose $n^\mbox{th}_{}$ (Error compiling LaTeX. Unknown error_msg) term is . Suppose that all of the terms of the sequence are , and that . Find .
Solution
Since the second differences are all and , can be expressed explicitly by the quadratic: .
Thus, .
Alternate Solution
Note that in every sequence of ,
Then
Since ,
Solving,
See also
1992 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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