  In this paper, we suggest a lower and an upper bound for the Generalized
Fibonacci-p-Sequence, for different values of p. The Fibonacci-p-Sequence is a
generalization of the Classical Fibonacci Sequence. We first show that the
ratio of two consecutive terms in generalized Fibonacci sequence converges to a
p-degree polynomial and then use this result to prove the bounds for
generalized Fibonacci-p sequence, thereby generalizing the exponential bounds
for classical Fibonacci Sequence. Then we show how these results can be used to
prove efficiency for data hiding techniques using generalized Fibonacci
sequence. These steganographic techniques use generalized Fibonacci-p-Sequence
for increasing number available of bit-planes to hide data, so that more and
more data can be hidden into the higher bit-planes of any pixel without causing
much distortion of the cover image. This bound can be used as a theoretical
proof for efficiency of those techniques, for instance it explains why more and
more data can be hidden into the higher bit-planes of a pixel, without causing
considerable decrease in PSNR.
