2023 AIME II Problems/Problem 1
Problem
The numbers of apples growing on each of six apple trees form an arithmetic sequence where the greatest number of apples growing on any of the six trees is double the least number of apples growing on any of the six trees. The total number of apples growing on all six trees is Find the greatest number of apples growing on any of the six trees.
Solution
In the arithmetic sequence, let be the first term and
be the common difference, where
The sum of the first six terms is
We are given that
The second equation implies that
Substituting this into the first equation, we get
It follows that
Therefore, the greatest number of apples growing on any of the six trees is
~MRENTHUSIASM
See also
2023 AIME II (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
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