2006 AMC 12A Problems/Problem 23
Problem
Given a finite sequence of
real numbers, let
be the sequence
of real numbers. Define
and, for each integer
,
, define
. Suppose
, and let
. If
, then what is
?
Solution
In general, such that
has
terms. Specifically,
To find x, we need only solve the equation
. Algebra yields
.