Question

If sixth term of a H.P. is $\frac{1}{61}$ and its tenth term is $\frac{1}{105}$, then first term of that H.P. is

• A. $\frac{1}{28}$
• B. $\frac{1}{39}$
• C. $\frac{1}{6}$
• D. $\frac{1}{17}$

Answer 1

The correct option is C

$\frac{1}{6}$

$T_6$ of H.P. = $\frac{1}{61}\Rightarrow T_6$ of A.P. = 61

and $T_{10}$ of H.P. = $\frac{1}{105}\Rightarrow T_{10}$ of A.P. = 105,

so, a + 5d = 61 ........(i) and a + 9d = 105 .....(ii)

From (i) and (ii), a= 6

Therefore first term of H.P. = $\frac{1}{a}$ = $\frac{1}{6}$.