The term 'become progressively weaker' can be summarized by the word 'TAPER, ' which is a five-letter word. TAPER means to gradually decrease in strength, intensity, or size. This term is often used to describe a gradual decrease in the size of something, such as a candle flame or a mountain range. It can also be used to describe a gradual decrease in the intensity of something, such as a sound or a feeling.