Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


Ari
Posts:
53
Registered:
1/25/05


Re: arithmetic progression that's also a geometric one, with a known largest number, need advice
Posted:
Jan 27, 2005 10:34 PM


"Edwill" <nosmapn@lamof.com> wrote in message news:ct6j3b$g3e$1@titan.btinternet.com... > Hi all, > > The problem is that an arithmetic progression (a_1,...,a_n), is also a geometric progression (after applying some permutation). > They (a_i's) are all different, and the largest number of them is 2004. > > Any idea to begin with to make a breakthrough? > > So far, > > 1). they have the same sum > 2). the series is either monotonic increasing, or decreasing > 3). if 2). is the case, and without loss of generality, can i assume a_n=2004. or am i already lost in 2).? > > Thank you very much...I just need some enlightening hint...:D >
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
A progression that is both arithmetic and geometric must be constant.
Aristotle Polonium
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +



