Modern society faces a significant challenge with the aging of the global population. The number of seniors is projected to surpass 1.4 billion by 2030, which will undoubtedly impact the sustainability of current healthcare systems, both in the public and the private sectors. To address some health issues that often face the elderly in terms of abnormal home behavior, or accidental falls, sensor-based systems for human activity recognition and automatic fall detection have become valuable tools which can be used for immediate notification to caregivers. These systems can monitor the health status of elderly individuals, promote healthy lifestyles, and provide timely medical intervention, leading to improved recovery and rehabilitation. In this paper, we propose a deep learning model that takes advantage of the affordability and latest technological advancements of mobile sensors to identify certain physical activities and promptly send an alert in the event of a fall. Our hybrid model combines the strength of Convolutional Neural Networks for feature extraction with the advantages of Long Short-Term Memory networks for time series forecasting and classification. Through experiments on two public datasets, we demonstrate the effectiveness of our approach, achieving superior performance in recognizing human activities and a high accuracy for fall detection, surpassing the performance of similar studies.