Direction for questions: Answer the questions based on the following information. A series $S_{1}$ of five positive integers is such that the third term is half the first term and the fifth term is $20$ more than the first term. In series $S_{2}$, the $n$th term defined as the difference between the $(n+1)$ term and the $n^{th}$ term of series $S_{1}$, is an arithmetic progression with a common difference of $30$.