Question

If n!, 3 × (n!) and (n + 1)! are in G.P, then the value of n will be

(a) 3 

(b) 4 

(c) 8 

(d) 10

Answer 1

(c) 8 

Given, n!, 3 × n! and (n + 1)! are in G.P 

⇒ (3 × n!)² = n! × (n + 1)!           (∵ a, b, c in G.P. ⇒ b² = ac) 

⇒ 9 × (n!)² = n! × (n + 1)! 

⇒ 9 × n! = (n + 1)! 

⇒ 9n! = (n + 1) . n!             (∵ n! = 1.2.3. ...... n) 

⇒ n + 1 = 9 ⇒ n = 8.