Compute the 16th term of HP if the 6th and 11th term of HP are 10 and 18, respectively.

To solve this problem, we first need to understand that the terms of a Harmonic Progression (HP) are the reciprocals of an Arithmetic Progression (AP).

Given that the 6th and 11th terms of the HP are 10 and 18 respectively, we can say that the 6th and 11th terms of the corresponding AP are 1/10 and 1/18 respectively.

Let's denote the first term of the AP as 'a' and the common difference as 'd'.

From the given information, we can write two equations:

a + 5d = 1/10 (since the 6th term is 1/10)

a + 10d = 1/18 (since the 11th term is 1/18)

Subtracting the first equation from the second, we get:

5d = 1/18 - 1/10

Solving this equation gives us the common difference 'd' of the AP.

Once we have 'd', we can substitute it back into the first equation to find 'a', the first term of the AP.

Finally, to find the 16th term of the HP, we find the 16th term of the AP (using the formula a + 15d), and then take its reciprocal.