Question

The $9th$ term of an AP is $499$ and $499th$ terms is $9.$ The term which is equal to zero is

• A. $501th$
• B. $502th$
• C. $508th$
• D. None of these

Answer 1

The correct option is C $508th$

$a_9=a+8d$
$a_9=499\left(given\right)$
$\therefore a+8d=\mathrm{499.........}\left(i\right)$
$a_{499}=a+498d$
$a_{499}=9$
$\therefore a+498d=\mathrm{9.........}\left(ii\right)$
Subtract (i) from (ii)
$\Rightarrow 490d=-490$
$\Rightarrow d=-1$
substitute the value of $d$
$\Rightarrow a+8(-1)=499$
$\Rightarrow a=507$
$\therefore$ For $a_n=0$
$\Rightarrow a+(n-1)d=0$
$\Rightarrow 507+(n-1)(-1)=0$
$\Rightarrow 507=n-1$
$\Rightarrow n=508$
So, ${508}^{th}$ term is equal to zero.