Question

The sixth term of a HP is 1/61 and the 10th term is 1/105. The first term of the H.P. is

Answer 1

6th term of HP = 1/61
6th term of related AP = 61
10th term of HP = 1/105
10th term of related AP = 105

let common difference of AP = d
a₆ = a₁ + 5d
⇒ 61 = a₁ + 5d -------------------(1)

a₁₀ = a₁ + 9d
⇒ 105 = a₁ + 9d  -------------------(2)

subtracting (1) from (2)
44 = 4d
⇒ d = 44/4 = 11

putting in equation (1)
61 = a₁ + 5 * 11
⇒ 61 = a₁ + 55
⇒ a₁ = 61-55 = 6
first term of AP = 6
So first term of HP = 1/6