Home Competitions AIME 2007b Problem 12
The increasing geometric sequence x 0 , x 1 , x 2 , … x_{0},x_{1},x_{2},\ldots x 0 , x 1 , x 2 , … 3. 3. 3. ∑ n = 0 7 log 3 ( x n ) = 308 \sum_{n=0}^{7}\log_{3}(x_{n}) = 308 ∑ n = 0 7 log 3 ( x n ) = 308 56 ≤ log 3 ( ∑ n = 0 7 x n ) ≤ 57 , 56 \leq \log_{3}\left ( \sum_{n=0}^{7}x_{n}\right ) \leq 57, 56 ≤ log 3 ( ∑ n = 0 7 x n ) ≤ 57 , log 3 ( x 14 ) . \log_{3}(x_{14}). log 3 ( x 14 ) .
Dataset text AIME 1983 to 2026 . Quoted with source.
Show the answer
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.
Add a solution
Locator aime/2007b/p12 · Tag 6J82Z3HXN3 · Edit this page on GitHub · Keys: j next, k previous