Question

The largest positive term of the HP, whose first two terms are $\frac{2}{5}$ and $\frac{12}{23}$ is

• A. $6$
• B. $\frac{13}{2}$
• C. $\frac{15}{2}$
• D. $9$

Answer 1

The correct option is A $6$

$\frac{5}{2},\frac{23}{12}$ are in $A\cdot P$

$a_n>0$

$a+(n-1)d>0$

$\frac{5}{2}+(n-1)\times -\frac{7}{12}>0(a=\frac{5}{2},d=\frac{23}{12}-\frac{5}{2}=\frac{-7}{12})$

$\frac{5}{2}>(n-1)\times \frac{7}{12}$

$30>7n-7\Rightarrow n<\frac{37}{7}$

$\Rightarrow n<5.2$

$\Rightarrow n=5$

$a_5=\frac{5}{2}+(5-1)\times \frac{-7}{12}=\frac{1}{6}=$ greatest term in A.P

$\therefore$ Greatest positive term in $H\cdot P^{}=6.$

Option is (A).