The driving force behind the generation of biological sequences are genomic mutations that shape these sequences throughout their evolutionary history. Due to the complexity of these processes, designing tractable stochastic models and analyzing them are challenging. We study two types of mutations, tandem duplication and substitution, which play a critical role in forming tandem repeat regions. We provide a stochastic model and, via stochastic approximation, study the behavior of the frequencies of k-mers in resulting sequences. Specifically, we show that k-mer frequencies converge almost surely to a set which we identify as a function of model parameters. From these frequencies, other statistics can be derived. In particular, we present a method for finding upper bounds on entropy.