Question

Find the 10th term of harmonic progression
$\frac{1}{5}$, $\frac{4}{19}$, $\frac{2}{9}$, $\frac{4}{17}\cdots \cdots$

Answer 1

Given, HP is $\frac{1}{5}$, $\frac{4}{19}$, $\frac{2}{9}$, $\frac{4}{17}\cdots \cdots$
$⟹5$, $\frac{19}{4}$, $\frac{9}{2}$, $\cdots \cdots$ are in AP
$⟹d=t_2-t_1=\frac{19}{4}-5=-\frac{1}{4}$
$a=5$, $d=-\frac{1}{4}$ and $t_n=a+(n-1)d⟹t_{10}=a+9d$
$=5+9\times -\frac{1}{4}=\frac{11}{4}$.