However, due to complexity, and since the user requested difficult Olympiad-style, this is acceptable.
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- So \( x = rac{ -35 + \sqrt{2041} }{4} \) (since \( x > 0 \))
- But to match format, we write:
- #### \( rac{-35 + \sqrt{2041}}{4} \)
- The sum of the first \( n \) terms of an arithmetic sequence is given by \( S_n = 3n^2 + 5n \). What is the common difference of the sequence?
- The sum formula: \( S_n = rac{n}{2} (2a + (n-1)d) \)
- Set equal: \( rac{n}{2} (2a + (n-1)d) = 3n^2 + 5n \)
