In online recommendation, financial service, etc., the most common application of multi-task learning (MTL) is the multi-step conversion estimations. A core property of the multi-step conversion is the sequential dependence among tasks. Most existing works focus far more on the specific post-view click-through rate (CTR) and post-click conversion rate (CVR) estimations, which neglect the generalization of sequential dependence multi-task learning (SDMTL). Besides, the performance of the SDMTL framework is also deteriorated by the interference derived from implicitly conflict information passing between adjacent tasks. In this paper, a systematic learning paradigm of the SDMTL problem is established for the first time, which can transform the SDMTL problem into a general MTL problem and be applicable to more general multi-step conversion scenarios with longer conversion path or stronger task dependence. Also, the distribution dependence between adjacent task spaces is illustrated from a theoretical point of view. On the other hand, an SDMTL architecture, named Task Aware Feature Extraction (TAFE), is developed to enable dynamic task representation learning from a sample-wise view. TAFE selectively reconstructs the implicit shared information corresponding to each sample case and performs explicit task-specific extraction under dependence constraints. Extensive experiments on offline public and real-world industrial datasets, and online A/B implementations demonstrate the effectiveness and applicability of proposed theoretical and implementation frameworks.