Question

If first two terms of a H.P. are $\frac{2}{5}$ and $\frac{12}{13}$ respectively, then the largest term is

• A. $\frac{14}{3}$
• B. $\frac{12}{13}$
• C. $\frac{13}{12}$
• D. $\frac{3}{14}$

Answer 1

Answer: (B)

$\frac{12}{13}$

if a,b,c are in H.P, then 1/a,1/b,1/c are in AP.

Let the third term be c.

Then, 5/2,13/12,1/c are in AP.

common difference d=13/12-5/2=-17/12 < 0 .(decreasing series)

13/12-5/2=1/c-13/12

13/6-5/2=1/c

1/c=-1/3

-1/3<0.

Since this is a decreasing AP, all the terms that come after the third term (c) are less than zero.

So their reciprocals are also less than zero.

Therefore the largest term in this series is 12/13.