Question

find the nth term of HP. 1/5, 1,-1/3, -1/7...​

Answer 1

Answer:

so this is the answer I think this is helpful

Answer 2

Given,

H.P = 1/5, 1, -1/3, -1/7

To Find,

The nth term of the given H.P. =?

Solution,

We can solve the question using the following steps:

We know,

If a,b,c,d,e are in harmonic progression, then their reciprocals, 1/a, 1/b, 1/c, 1/d, 1/e, are in arithmetic progression.

Here, 1/5, 1, -1/3, -1/7 are in HP. Then, 5, 1, -3, -7 are in AP.

Now,

nth term of AP, $T_{n} = a + (n - 1)d$

$a = 5\\d = 1 - 5 = -4$

Substituting the values,

$T_{n} = 5 + (n - 1)(-4)$

     $= 5 + (-4n) + 4$

      $= 9 - 4n$

Now, the nth term of HP is $\frac{1}{T_{n} }$

$\frac{1}{T_{n} } = \frac{1}{9-4n}$

Hence, the nth term of the HP is $\frac{1}{9-4n}$.