The train holds 66 passengers It starts out empty It picks up 1 passenger at the first station 2 passengers at the second station 3 passengers at the third station and so on No one gets off?

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.