Difference between revisions of "2016 AIME II Problems/Problem 9"
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Revision as of 20:23, 17 March 2016
The sequences of positive integers 
and 
are an increasing arithmetic sequence and an increasing geometric sequence, respectively. Let 
. There is an integer 
such that 
and 
. Find 
.
Solution
Since all the terms of the sequences are integers, and 100 isn't very big, we should just try out the possibilities for 
. When we get to 
and 
, we have 
and 
, which works, therefore, the answer is 
.
