Question

If the harmonic mean of 2,a,8 be 24/7,then the value of a be:

Answer 1

Given,

The harmonic mean of three numbers: 2, a, 8 is = 24/7

To find,

The value of a.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

If x, y, and z are three numbers in harmonic progression, then their harmonic mean is calculated as:

H.P. = 3/{1/x + 1/y + 1/z}

Now, according to the question;

The harmonic mean of three numbers: 2, a, 8 is = 24/7

=> 3/{1/2 + 1/a + 1/8} = 24/7

=> 24×{1/2 + 1/a + 1/8} = 3×7

=> {1/2 + 1/a + 1/8} = 7/8

=> 1/a = 7/8 - 1/8 - 1/2 = 7/8 - 1/8 - 4/8

=> 1/a = 2/8 = 1/4

=> a = 4

Hence, the value of a is equal to 4.