Question

The 4^th term of a H.P. is $\frac{3}{5}$ and 8^th term is $\frac{1}{3}$ then its 6^th term is

• A. $\frac{1}{6}$
• B. $\frac{3}{7}$
• C. $\frac{1}{7}$
• D. $\frac{3}{5}$

Answer 1

Answer: (B)

$\frac{3}{7}$

Answer 2

Let $\frac{1}{a},\frac{1}{a + d},\frac{1}{a + 2d},.......$ be an H.P.

$\therefore$ 4^th term $= \frac{1}{a + 3d}$ ⇒ $\frac{3}{5} = \frac{1}{a + 3d}$

⇒ $\frac{5}{3} = a + 3d$ …..(i)

Similarly, $3 = a + 7d$ …..(ii)

From (i) and (ii), $d = \frac{1}{3}$, $a = \frac{2}{3}$

∴ 6^th term $= \frac{1}{a + 5d} = \frac{1}{\frac{2}{3} + \frac{5}{3}} = \frac{3}{7}$