Retrieval-Augmented Generation (RAG) is a promising technique for mitigating two key limitations of large language models (LLMs): outdated information and hallucinations. RAG system stores documents as embedding vectors in a database. Given a query, search is executed to find the most related documents. Then, the topmost matching documents are inserted into LLMs’ prompt to generate a response. Efficient and accurate searching is critical for RAG to get relevant information. We propose a cost-effective searching algorithm for retrieval process. Our progressive searching algorithm incrementally refines the candidate set through a hierarchy of searches, starting from low-dimensional embeddings and progressing into a higher, target-dimensionality. This multi-stage approach reduces retrieval time while preserving the desired accuracy. Our findings demonstrate that progressive search in RAG systems achieves a balance between dimensionality, speed, and accuracy, enabling scalable and high-performance retrieval even for large databases. Our code is available at https://github.com/taeheej/Progressive-searching-for-Retrieval-in-RAG.