Alzheimer disease and other dementias have become the 7th cause of death worldwide. Still lacking a cure, an early detection of the disease in order to provide the best intervention is crucial. To develop an assessment system for the general public, speech analysis is the optimal solution since it reflects the speaker's cognitive skills abundantly and data collection is relatively inexpensive. While most of the related studies extracted statistics-based features and relied on a feature selection process, we have proposed a novel Feature Sequence representation and utilized a recurrent neural network to perform classification in this paper. To validate our work, an experiment has been conducted with 150 speech samples, and the score in terms of the area under the receiver operating characteristic curve is as high as 0.954, potentially outperforming the current state-of-the-art method.