Question

If the coefficients of 5th, 6th, and 7th terms in the expansion of (1 + x)ⁿ are in A.P., then n equals

(a) 7 

(b) 5 

(c) 3 

(d) 10

Answer 1

Answer : (a) 7

(1 + x)ⁿ = ⁿC₀ + ⁿC₁ x + ⁿC₂ x² + ..... + ⁿC_{n – 1} x^{n – 1} + ⁿC_n xⁿ 

Given, coefficients of 5th, 6th and 7th terms are in A.P. 

⇒ ⁿC₄, ⁿC₅, ⁿC₆ are in A.P ⇒ 2 . ⁿC₅ = ⁿC₄ + ⁿC₆