Let the coefficients of the middle terms in the expansion of 1 6 + β x 4 , 1 - 3 β x 2 and 1 - β 2 x 6 , β > 0 , respectively form the first three terms of an A.P. If d is the common difference of this A.P., then 50 - 2 d β 2 is equal to _____ .

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Let the coefficients of the middle terms in the expansion of 1 6 + β x 4 , 1 - 3 β x 2 and 1 - β 2 x 6 , β > 0 , respectively form the first three terms of an A.P. If d is the common difference of this A.P., then 50 - 2 d β 2 is equal to _____ . Given, Coefficients of middle terms of given expansions 1 6 + β x 4 , 1 - 3 β x 2 and 1 - β 2 x 6 are C 2 4 1 6 β 2 ,   C 1 2 - 3 β   &   C 3 6 - β 2 3 respectively, Now it is given that middle te