Question

Find the $n^{th}$ term of the H.P. $\frac{1}{20},\frac{1}{30},\frac{1}{40}....$ $-\frac{1}{100}$ is

• A. $\frac{1}{11}$
• B. $\frac{-1}{11}$
• C. $\frac{-1}{12}$
• D. $\frac{2}{11}$

Answer 1

The correct option is B $\frac{-1}{11}$

The reciprocal of A.P. is H.P.
A.P. is in the form of $20,30,40,...$
Let the general form of A.P., $a_n=a+(n-1)d$
Common difference, $d=10$
$a_n=-100$
$a_n=a+(n-1)d$
$-100=20+(n-1)\times 10$
$-100-20=10n-10$
$-120+10=10n$
$-110=10n$
$n=-11$
Therefore, $n^{th}$ term of H.P. is $\frac{-1}{11}$.