A series of numbers is said to be in harmonic sequence if the reciprocals of all the terms of the sequence form an arithmetic sequence.
*Remember the reciprocal of $a$ is $\dfrac{1}{a}$ meaning the reciprocal of $\dfrac{1}{3}$ is $3$. To test whether two numbers are reciprocals of each other, simply multiply them and if the answer is $1$ then it implies they pass the reciprocal test.
For example:
The sequence
\[\dfrac{1}{4};\dfrac{1}{6};\dfrac{1}{8};\dfrac{1}{10};\dfrac{1}{12};...\]
So what we have to do is to prove that the reciprocals of the terms in the sequence form an arithmetic sequence.
The reciprocals are as follows:
\[4;6;8;10;12;...\]
*Whenever you are given Harmonic Progression convert it into A.P