Question

What is the $n^{th}$ term of the harmonic sequence $\frac{1}{2},\frac{1}{4},\frac{1}{6},\frac{1}{8}$?

• A. $\frac{1}{n}$
• B. $\frac{1}{2n}$
• C. $\frac{1}{3n}$
• D. $\frac{1}{4n}$

Answer 1

The correct option is B $\frac{1}{2n}$

Given sequence is $\frac{1}{2},\frac{1}{4},\frac{1}{6},\frac{1}{8}$

$n^{th}$ term of the corresponding AP will be:

$a+(n-1)d$

Here $a=2$ and $d=2$

$n^{th}$ term of the corresponding AP will be:

$=2+(n-1)2=2+2n-2=2n$

Thus $n^{th}$ term of the HP will be $\frac{1}{2n}$.