Book Maths Puzzle

A sequence of numbers is represented as a1,a2,a3,....,an. Each number in the sequence (except the first and the last) is the mean of the two adjacent numbers in the sequence. If a1=1 and a5=3,what is the value of a3 ?

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Book Other Question

An old man distributed all the coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 36 times the difference between the two numbers. How many coins did the old man have? What is the smallest positive integer k such that (2000)(2001)k is a perfect sqaure ?