Question

The 12th and 19th terms of a harmonic progression are respectively \(\frac{1}{5}\) and \(\frac{3}{22}\). Then the 4th term of the progression is
1. \(\frac{3}{7}\)
2. \(\frac{7}{3}\)
3. \(\frac{1}{3}\)
4. \(\frac{4}{3}\)

Answer 1

Correct Answer - Option 1 : \(\frac{3}{7}\)

Concept:

n^th term of AP is given by

T_n = a + (n - 1)d

Where a and d are first term and common difference respectively.

Note: Harmonic progression (HP) is the reciprocal of the values of the terms in arithmetic progression(AP). 

Calculation:

Given that

12^th term of AP = 5

19^th term of AP = 22/3

⇒ a + 11 d = 5      ----(1)

⇒ a + 18d = 22/3   ----(2)

Subtracting equation (2) from equation (1), we will get

7d = 7/3

d = 1/3

Hence, from equation (1),

a = 4/3

Therefore 4^th term of AP

= a + 3d = 7/3

Hence 4th term of HP = 3/7