Difference between revisions of "1998 AIME Problems/Problem 8"
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Except for the first two terms, each term of the sequence <math>1000, x, 1000 - x,\ldots</math> is obtained by subtracting the preceding term from the one before that. The last term of the sequence is the first [[negative]] term encounted. What positive integer <math>x</math> produces a sequence of maximum length? | Except for the first two terms, each term of the sequence <math>1000, x, 1000 - x,\ldots</math> is obtained by subtracting the preceding term from the one before that. The last term of the sequence is the first [[negative]] term encounted. What positive integer <math>x</math> produces a sequence of maximum length? | ||
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== See also == | == See also == | ||
{{AIME box|year=1998|num-b=7|num-a=9}} | {{AIME box|year=1998|num-b=7|num-a=9}} | ||
Latest revision as of 02:01, 25 August 2024
Problem
Except for the first two terms, each term of the sequence 
is obtained by subtracting the preceding term from the one before that. The last term of the sequence is the first negative term encounted. What positive integer 
produces a sequence of maximum length?
Solutions were removed
Contents
See also
| 1998 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
