If the eleventh term in the binomial expansion of (x+a)¹⁵ is the geometric mean of the eighth and twelfth terms, then the greatest term in the expansion is

Step-by-step solution

From the given condition T₁₁= T₈ T₁₂ aligned & ( 15 10 x^5 a¹⁰ )= ( ¹⁵ C₇ x^8 a^7 ) ( 15 11 x^4 a¹¹ ) & x a = 77 75 aligned Now, greatest term = cases T_p and T_ p+1 ; & if n+1 | x a |+1 =p is an integer T_ q+1 & ; if n+1 | x a |+1 is non integer and (q, q+1) cases So, n+1 | x a |+1 = 16 77 75 +1 (7,8) Greatest term = T ₈ i., e., 8^ th term.