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Lets change the sum to a achievable number.
But the instruction is to generate based on persona, so I can adjust.
But the problem says is 1200, so perhaps make it 1150.
But to proceed, lets use a different sum.
Alternatively, accept that in some contexts, they solve the quadratic.
But for accuracy, lets use a sum that is achieved.
But to fix, lets use a new sequence.
The sum of an arithmetic sequence is 1260. First term 10, common difference 5. Find n.
But for the sake of the task, Ill use the calculation with 1200, accept the n=20.465, but since its number of widgets, perhaps the answer is 20, but sum not 1200.
Perhaps the question allows non-integer, but no.
