Writo's Arithmetic Progression

Calculus Level 3

If a1,a2,a4001a_1, a_2, \cdots a_{4001} are in Arithmetic Progression

and 1a1a2+1a2a3++1a4000a4001=10\frac{1}{a_1 a_2} + \frac{1}{a_2 a_3} + \cdots + \frac{1}{a_{4000} a_{4001}} = 10

and a2+a4000=50a_2 + a_{4000} = 50

Evaluate a1a4001 | a_1 - a_{4001} |

Thanks to @Writo for this problem
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