Question

If a, a₁ , a₂ , a₃ , ..........,a_2n, b are in AP and a, g₁ , g₂ , g₃ , .....................g_2n, b are in G..P. and h is the single harmonic mean of a & b, then a₁ + a_2n/g₁g_2n + a₂ + a_2n - 1/g₂g_{2n -1} + a_n + a_{n + 1}g_ng_{n + 1} is equal to

(a)  2n/h

(b)  2nh

(c)  nh

(d)  n/h 

Answer 1

Correct option (a) 2n/h

Explanation:

a₁ + a_2n =  a₂ + a_2n–1 =......................= a_n +a_n+1 = a+b and g₁g_2n 

= g₂.g_2n–1 =.....................= g_n .g_n+1 = ab

Also h = 2ab/ a + b

Given expression  = a + b/ab + a + b/ab + ........a+b/ab(n times)

= n a + b/ab = n.2/h = 2n/h