Question

If the $nth$ term of the AP $9,7,\mathrm{5..}$ is same as the $nth$ term of the AP $15,12,9,...$, find $n.$

• A. $7$
• B. $8$
• C. $9$
• D. $10$

Answer 1

The correct option is A $7$

$nth$ term of A.P $9,7,\mathrm{5....}=a+(n-1)d$
$\Rightarrow 9+(n-1)-2$
$\Rightarrow 9-2n+2\Rightarrow 11-2n$
$nth$ term of A.P $15,12,9,....=a+(n-1)d$
$\Rightarrow 15+(n-1)-3$
$\Rightarrow 15-3n+3\Rightarrow 18-3n$
$\therefore 11-2n=18-3n$
$\Rightarrow 3n-2n=18-11$
$\Rightarrow n=7$