RMO Part -4!

Let a 1 , a 2 , a 3 , a 4 , a 5 , . . . . . a m a_1,a_2,a_3,a_4,a_5,.....a_m be a sequence of real numbers.In a finite sequence of real numbers the sum of every seven successive numbers is negative and sum of every eleven successive numbers is positive.

Find the largest number of terms in such a sequence.


The answer is 16.

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