Examples on Harmonic Progression

Q1.

Write H.P. of a corresponding A.P. whose first term is 1 and common difference is 2

Sol.

Given that first term of A.P. = 1, common difference = 2.

i.e, a = 1, d = 2

We know that if a is the first term and d is the common difference of an A.P., then the H.P. is given by

.......

= 1 / 1, 1 / (1 + 2), 1 / (1 + 2(2))......

= 1, 1 / 3, 1 / 5.....

Q2.

The 4^th term of an H.P. is 2/3 and 7^th term is 2/5. Find 10^th term

Sol.

Given that, 4^th term = 2/3 and 7^th term = 2/5.

⇒ t₄ = 2/3 and t₇ = 2/5

2(a + 3d) = 3, and 2(a + 6d) = 5

Thus, 2a + 6d = 3 ------- (i)

and 2a + 12d = 5 ------- (ii)

By solving equations (i) and (ii) we get a, d values.

∴ a = 1 / 2 and d = 1 / 3

Now, 10^th term is