If 2 ,   h 1 ,   h 2 , . . . . . ,   h 20 ,   6 are in harmonic progression and 2 ,   a 1 ,   a 2 , . . . . ,   a 20 ,   6 are in arithmetic progression, then the value of a 3 h 18 is equal to

Step-by-step solution

1 2 , 1 h 1 , 1 h 2 , . . . . , 1 h 20 , 1 6 are in A.P. ⇒ 1 6 = 1 2 + 21 d ⇒ 1 6 - 1 2 21 = d ⇒ d = - 1 63 ⇒ 1 h 18 = 1 2 + 18 d = 1 2 + 18 2 - 1 63 7 = 1 2 - 2 7 1 h 18 = 3 14 ⇒ h 18 = 14 3 Also, 2 , a 1 , a 2 , . . . . . , a 20 , 6 are in A . P . ⇒ 6 = 2 + 21 D ⇒ D = 4 21 ⇒ a 3 = 2 + 3 D = 2 + 3 × 4 21 7 = 18 7 ⇒ a 3 h 18 = 18 6 7 × 14 2 3 = 1 2