Question

If the first 2 terms of H.P are $\frac{4}{11}$ and $\frac{2}{3}$ respectively, then the largest term is _____

• A. 2nd term
• B. 3rd term
• C. 4th term
• D. Can't be determined

Answer 1

The correct option is B

3rd term

Given $\frac{4}{11}$, $\frac{2}{3}$ are in H.P.

$\Rightarrow$ $\frac{11}{4}$, $\frac{3}{2}$ form A.P.

Common difference D = $\frac{3}{2}$ - $\frac{11}{4}$ = $\frac{-5}{4}$

Nth term of H.P. = $\frac{1}{\frac{11}{4}+(n-1)\left(\frac{-5}{4}\right)}$ [nth term = $\frac{1}{a+(n-1)d}$]

= $\frac{4}{16-5n}$

For nth term of H.P. to be largest, 16 - 5n has to take minimum positive value. This is possible for n = 3

So, 3rd term is the largest term.