Question

The first term of a H P whose second term is $\frac{5}{2}$ and third term is $\frac{10}{3}$, is___

Answer 1

Let $x$ be the first term of H.P.

$x,\frac{5}{2},\frac{10}{3}$ are in H.P.

$\Rightarrow$ $\frac{1}{x},\frac{2}{5},\frac{3}{10}$ are in A.P.

So, $\frac{2}{5}-\frac{1}{x}=\frac{3}{10}-\frac{2}{5}$

$-\frac{1}{x}=\frac{3}{10}-\frac{4}{5}$

$\frac{1}{x}=\frac{1}{2}$

$x=2$

So, the first term = 2