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Re-express: perhaps the problem assumes exact arithmetic.
But 1200 is likely a typo or accept the quadratic solution.
However, in real exams, such models expect algebraic solution even if not integer.
But terms must be integer. So likely, the sum is meant to be achieved.
But in exact math, no integer solution.
But problem says is 1,200, so perhaps accept the equation and find positive root.
But number of terms must be integer.
Alternatively, perhaps the sequence is defined to have exact sum.
But given the format, likely expects solving the quadratic and taking ceiling or floor.
However, in standard problems, such sums are structured to be exact.