Question

Find the 10th term of the H.P: $1,\frac{1}{3},\frac{1}{5},\frac{1}{7},\frac{1}{9},\frac{1}{11},....$

• A. 19
• B. $\frac{1}{19}$
• C. 21
• D. $\frac{1}{21}$

Answer 1

Answer: (B)

$\frac{1}{19}$

$t_n=\frac{ab}{b+(n-1)(a-b)}$

Here $a=1,b=\frac{1}{3}$, $n=10$

$t_n=\frac{1\times \frac{1}{3}}{\frac{1}{3}+(10-1)(1-\frac{1}{3})}$

$\Rightarrow \frac{\frac{1}{3}}{\frac{1}{3}+9\times \frac{1}{3}}$

$\Rightarrow \frac{\frac{1}{3}}{\frac{1}{3}+6}$

$\Rightarrow \frac{\frac{1}{3}}{\frac{19}{3}}$

$\Rightarrow \frac{1}{3}\times \frac{3}{19}\Rightarrow \frac{1}{19}$