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The train picks up passengers in an increasing sequence: 1 at the first station, 2 at the second, 3 at the third, and so on. The total number of passengers picked up can be calculated using the formula for the sum of the first ( n ) integers: ( S = \frac{n(n + 1)}{2} ). To find when the train reaches its capacity of 66 passengers, we solve for ( n ) in the equation ( \frac{n(n + 1)}{2} = 66 ). Solving this gives ( n = 11 ), meaning the train will be full after picking up passengers at the 11th station.

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1w ago

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