Question

the tenth term of H. P. 2/9, 1/7, 2/19, 1/12...is​

Answer 1

Answer:

10th term of h.p. is 1/27

Answer 2

We have to find the tenth term of H.P ; 2/9 , 1/7 , 2/19 , 1/12 ...

Harmonic progression :

• Harmonic progression is a progression which is formed by taking the reciprocal of arithmetic progression.
• for example, if 1/a₁ , 1/a₂ , 1/a₃ 1/a₄ .... are in Harmonic progression then, a₁ , a₂ , a₃ , a₄ ... are in arithmetic progression.

now here sequence is ..

2/9 , 1/7 , 2/19 , 1/12 ...

just take reciprocal of each terms of the given sequence, we will get arithmetic progression.

i.e., 9/2 , 7/1 , 19/2 , 12/1 ... are in AP.

(7/1 - 9/2) = (19/2 - 7/1) = (12 - 19/2) = 5/2

hence common ratio , d = 5/2

first term, a = 9/2

we know, nth term in AP , Tn = a + (n - 1)d

∴ 10th term = T₁₀ = 9/2 + (10 - 1) × 5/2 = 27

∴ 10th term of HP = 1/10th term of AP = 1/27

Therefore the 10th term of given HP is 1/27.