Question

If second and seventh terms of H.P . are $\frac{1}{5}$ and $\frac{1}{25}$ then first term is

Answer 1

Given,

$h_2=\frac{1}{5}\Rightarrow a_2=5$

$h_7=\frac{1}{25}\Rightarrow a_7=25$

Therefore,

$a+d=5$....(1)

$a+6d=25$.....(2)

On solving (1) and (2), we get,

$d=4$

From (1)

$a=1$

$\therefore h=1$, first term

hence, this is the answer.