Question

Which term of the A.P.,$-9,-8.25,-\mathrm{7.5....}$ is its first positive term?

• A. $12$
• B. $13$
• C. $14$
• D. $15$

Answer 1

The correct option is C $14$

$a=-9,$ $d=(-8.25-(-9))=\frac{+3}{4}=\mathrm{0.75.}$

Let $T_n$ is positive

$\Rightarrow T_n=-9+(n-1)0.75$

$T_n>0$

$\Rightarrow -9+(n-1).75>0$

$.75n-.75>9$

$.75n>9.75$

$n>\frac{9.75}{.75}$

$n>13$

Hence $13th$ term is $0-$

$14th$ term is positive $-$

Hence, the answer is $14.$