Correct Option: A

The 1st term of an HP is 1/17 .
Hence, for the corresponding AP, the terms is 17 .
Here, a = 17
nth term of an AP is given by T_n = a + (n -1)d
∴ T₂ = 17 + d, T₄ = 17 + 3d
T₅ = 17 + 4d, T₆ = 17 + 5d
∴ (17 + d) (17 + 3d) = (17 + 4d) (17 + 5d)
⇒ 289 + 51d + 17d + 3d² = 289 + 85d + 68d + 20d²
⇒ 68d + 3d² = 153d + 20d²
⇒ 17d² = -85d
⇒ d = -5
∴ 3rd term is T₃ = a + 2d = 17 + 2(-5)
= 17 - 10 = 7
Hence, for the corresponding HP, the 3rd term is 1/7.