Question

Which of the following are harmonic progressions.

(a)

(b)

(c)

(d)

Answer 1

(a) The given sequence is

Taking reciprocal of every term, we get 1, 3, 5, 7 …

These terms form an A.P. with and .

Thus, is in H.P.

(b) The given sequence is

Taking reciprocal of every term, we get 1, 3, 6, 12 ….

These terms do not form an A.P. [3 − 1 = 2, 6 − 3 = 3]

Thus, is not in H.P.

(c) The given sequence is

Taking reciprocal of every term, we get .

These terms form an A.P with and .

Thus, is in H.P.

(d) The given sequence is

Taking reciprocal of every term, we get 2, 5, 10, 17 …..

These terms do not form an A.P. [5 − 2 = 3, 10 − 5 = 5].

Thus, is not in H.P.