If $$a1$$,$$a2$$,$$a3$$,…,$$a4001are$$ term of an AP such that $$1a1a2+1a2a3+$$…$$+1a4000a4001=10a2$$ and $$a2+a4000=50$$, then $$a1$$−$$a4001is$$ equal to

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If $$a1$$,$$a2$$,$$a3$$,…,$$a4001are$$ term of an AP such  that $$1a1a2+1a2a3+$$…$$+1a4000a4001=10a2$$ and  $$a2+a4000=50$$, then $$a1$$−$$a4001is$$ equal to

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Now,$$1a1a2+1a2a3+$$…$$+1a4000a4001=1da2$$−$$a1a1a2+a3$$−$$a2a2a3+$$…$$+a4001$$−$$a4000a4000a4001=1d1a1$$−$$1a2+1a2$$−$$1a3+$$…$$+1a4000$$−$$1a4001=1d1a1$$−$$1a4001=4000a1a4001=10$$       (given) ⇒ $$a1a4001=400$$                              ...(i)            $$a1+a4001=a2+a4000=50$$                .....(ii)∴ $$a1$$−$$a40012=a1+a40012$$−$$4a1a4001=(50)2$$−$$1600$$⇒ $$a1$$−$$a4001=30$$

If $a_{1}, a_{2}, a_{3}, \dots, a_{4001}$ are term of an AP such that $\frac{1}{a_{1} a_{2}} + \frac{1}{a_{2} a_{3}} + \dots + \frac{1}{a_{4000} a_{4001}} = 10 a_{2}$ and $a_{2} + a_{4000} = 50$ , then $|a_{1} - a_{4001}|$ is equal to

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If a1,a2,a3,…,a4001are term of an AP such that 1a1a2+1a2a3+…+1a4000a4001=10a2 and a2+a4000=50, then a1−a4001is equal to

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If $a_{1}, a_{2}, a_{3}, \dots, a_{4001}$ are term of an AP such that $\frac{1}{a_{1} a_{2}} + \frac{1}{a_{2} a_{3}} + \dots + \frac{1}{a_{4000} a_{4001}} = 10 a_{2}$ and $a_{2} + a_{4000} = 50$ , then $|a_{1} - a_{4001}|$ is equal to