(i) Which of the following statements is correct ? (a) G1 > G2 > G3 >........... (b) G1 < G2 < G3 <...........

Question

Read the following paragraph and answer the questions.

Let A₁, G₁, H₁ denote the A.M., G.M., H.M of two distinct positive numbers.

For n ≥ 2, let A_n–1 and H_n–1 have A.M., G.M., H.M as A_n, G_n, H_n respectively. 

(i) Which of the following statements is correct ?

(a) G₁ > G₂ > G₃ >...........

(b) G₁ < G₂ < G₃ <...........

(c) G₁ = G₂ = G₃ >...........

(d) G₁ < G₃ < G₅ < ........... and G₂ > G₄ > G₆ >......

(ii) Which are of the following statement is correct ?

(a) A₁ > A₂ > A₃ >............

(b) A₁ < A₂ < A₃ <............

(c) A₁ > A₃ > A₅ > ............. and A₂ < A₄ < A₆ < ........

(d) A₁ < A₃ < A₅ < ............. and A₂ > A₄ > A₆ > ........

(iii) Which are of the following statement is correct ?

(a) H₁ > H₂ > H₃ > ............

(b) H₁ < H₂ < H₃ < .............

(c) H₁ > H₃ > H₅ > ............... and H₂ < H₄ < H₆ < ............

(d) H₁ < H₃ < H₅ < .............. and H₂ > H₄ > H₆ > ..............

Answer 1

(i) (c) G₁ = G₂ = G₃ >...........

(ii) (a) A₁ > A₂ > A₃ >............

(iii) (b) H₁ < H₂ < H₃ < .............