Question

The 10th term of H.P. 1\2 , 2\5 , 1\3 , 2\7-------- is *​

Answer 1

1/2,2/5,1/3,2/7.is

answer

=1/9

Answer 2

We have to find the 10th term of HP ; 1/2 , 2/5 , 1/3 , 2/7 ....

let's rearrange it at first,

2/4 , 2/5 , 2/6 , 2/7 . ... ..

we know, if a , b , c , d ... are in Harmonic progression

then, 1/a , 1/b , 1/c , 1/d ... are in arithmetic progression.

so 4/2 , 5/2 , 6/2 , 7/2 ... are in arithmetic progression.

now you know nth term of an ap , Tn = a + (n - 1)d

where a is first term and d is common difference.

here a = 4/2 and d = 5/2 - 4/2 = 1/2

so 10th term = 4/2 + (10 - 1) × 1/2

= 4/2 + 9/2

= 13/2

hence 10th term in Ap = 13/2

therefore 10th term in HP = 2/13