Question

If a, a1 , a2 , a3 , ..........,a2n, b are in AP and a, g1 , g2 , g3 , .....................g2n, b are in G..P. and h is the single harmonic mean of a & b, then a1 + a2n/g1g2n + a2 + a2n - 1/g2g2n -1 + an + an + 1gngn + 1is equal to

(a) 2n/h

(b) 2nh

(c) nh

(d) n/h

Answer 1

Correct option (a) 2n/h

Explanation:

a1 + a2n = a2 + a2n–1 =......................= an +an+1 = a+b and g1g2n

= g2.g2n–1=.....................= gn .gn+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