Question

10th term of an harmonic progression is third and fifth terms are respectively 1 and 1 by minus 5​

Answer 1

Given : third and fifth terms  of Harmonic progression 1  &  1 /(-5)

To find :  10th term of   harmonic progression

Solution:

Harmonic Progression

1/a  , 1/(a + d)  ,  1/(a + 2d) , .............................. 1/(a + (n-1)d)

3rd term   = 1/(a + 2d)  =  1

=> a + 2d = 1

5th term = 1/(a + 4d) = 1/-5

=> a + 4d = - 5

2d  =  - 6

=> d = - 3

a + 2(-3) = 1

=> a = 7

a = 7  , d = - 3

10th term = 1/(a + 9d)

= 1/ (7 + 9(-3))

= 1/ (-20)

= - 1/20

- 1/20  is 10th term of  harmonic progression

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