Question

10th term of the Harmonic Progression $1,\frac{1}{3},\frac{1}{5},\frac{1}{7},\frac{1}{9},\frac{1}{11},...$ is $\frac{1}{k}$. Find k

Answer 1

$1,\frac{1}{3},....$ are in H.P.

$\Rightarrow 1,3,5,...$ are in A.P

$\Rightarrow a_1=1$ & $d=2$

$\therefore a_{10}=1+9\times 2=19$

$\therefore {10}^{th}$ term is $\frac{1}{19}$

$\Rightarrow k=19$.