Tips And Tricks And Shortcuts For Harmonic Progression

Tips and Tricks & shortcuts on  harmonic progression (HP)

Here, are some easy tips and tricks for you on HP with easily, and efficiently used tricks in competitive and recruitment exams.

There are 2 types of questions asked in exams

Type 1: Find nth term of series

Question 1

Find the 8th term in the series 1/2, 1/4, 1/6…….

Options:

A. 1/20

B.1/14

C.1/16

D. 1/18

Solution:

We know that,

tn = 1/a + (n – 1)d

Convert the HP series in AP

We get 2, 4, 6,……
In the given series,

a (first term) = 2

d (common difference) = 2 …. (4 – 2)

Therefore, 8th term = t8 = a + (n-1) d

t8 = 2 + (8– 1) 2

t8 = 2 + 7 * 2

t8 = 2 + 14

t8 = 16

Correct option: C

tips and tricks and shortcuts for harmonic progression

Type 2: Find the Harmonic mean of the series.

Question 1.

Find the harmonic mean (HM) of 8, 9, 6?

Options:

A. 4.55

B.6.65

C. 7.56

D. 7.46

Solution:

We know that,

HM = n/{1+a1+1/a2…1/an}

HM = 3/{1/8+1/9+1/6}

HM = 3/0.402

HM = 7.46

Correct option: D

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