1. The value of n is

Question

Let A₁, A₂, A₃, …, Am be the arithmetic means between -2 and 1027 and G₁, G₂, G₃, …, G_n be the geometric means between 1 and 1024. Product of the geometric means is 2⁴⁵ and the sum of arithmetic means is 1025 x 171.

1.  The value of n is

(A)  7

(B)  9 

(C)  11

(D)  None of these

2.  The value of m is

(A)  340

(B)  342

(C)  344

(D)  346

3.  The value of G₁ + G₂ + G3 + . . . + G_n is

(A)  1022

(B)  2044 

(C)  512

(D)  None of these

Answer 1

Correct answer  1. (B) 2.(B) 3. (A)

1. G₁ G₂… G_n

2.  A₁ + A₂ + A₃ + … + A_m-1 + A_m = 1025 x 171

Therefore, m (-2 + 1027/2) =  1025 x 171 ⇒ m = 342

3.  Since n = 9, therefore