Up, up and away

Algebra Level 5

Suppose 20152015 people of different heights are arranged in a straight line from shortest to tallest such that

(i) the tops of their heads are collinear, and

(ii) for any two successive people, the horizontal distance between them is equal to the height of the shorter of the two people.

If the shortest person is 4949 inches tall and the tallest is 8181 inches tall, then how tall is the person at the middle of the line, (in inches)?


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