Question

If the first two terms of an HP be $\frac{2}{5}$ and $\frac{12}{23}$ then the largest positive term of the progression is the

• A. 6th term
• B. 7th term
• C. 5th term
• D. 8th term

Answer 1

Answer: (C)

5th term

Given $\frac{2}{5},\frac{12}{23}$ are first and second term in HP

$\Rightarrow \frac{5}{2},\frac{23}{12}$ are in AP

$\therefore$ common difference $=\frac{23}{12}-\frac{5}{2}=\frac{-7}{12}$

Now, to find maximum n for which $\frac{5}{2}+(n-1)\left(\frac{-7}{12}\right)>0$

$\Rightarrow \frac{37}{12}-\frac{7n}{12}>0$

$\Rightarrow 7n<37\Rightarrow n=5$

$(\because$ smallest positive term of AP will be largest positive term of corresponding HP$)$
$\therefore$ Option C is correct