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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 $30$. 


What is the sum of series $S_{2}$?

  1. $10$ 
  2. $20$ 
  3. $30$ 
  4. $40$
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