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