A calculus problem by Shivam Jadhav

Calculus Level 4

If \[a_{1},a_{2},a_{3},........,a_{n}\] is a sequence of positive numbers which are in A.P with common difference 'd' and \[a_{1}+a_{4}+a_{7}+.......+a_{16}=147\], then \[a_{1}+a_{16}=M\] \[a_{1}+a_{6}+a_{11}+a_{16}=N\] Maximum value of \[a_{1}a_{2}......a_{16}=(\frac{S}{W})^{16}\] here S and W are co-prime non-negative integers. Find \[S+W+M+N\]

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