2016 AIME II Problems/Problem 9
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
.
Solution by Shaddoll