If the coefficients of x4,x5 and x6 in the expansion of (1 + x)n are in the arithmetic progression. Then the maximum value of n is.

Engineering

Mathematics

Arithmetic Progression and Its Properties

Introduction to Binomial Theorem

Question

If the coefficients of x⁴^,x⁵ and x⁶ in the expansion of (1 + x)ⁿ are in the arithmetic progression. Then the maximum value of n is.

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ⁿC₄, ⁿC₅, ⁿC₆ are in A.P.

2 (ⁿC₅) = ⁿC₄+ ⁿC₆ ⇒ n²– 21n + 98 = 0

(n – 14)(n – 7) = 0 ⇒ n = 7,14

maximum value of n=14