Question

If $5$ times the $5^{th}$ term of an $A.P$ is equal to $9$ times its $9^{th}$ term then its ${14}^{th}$ term is

• A. $0$
• B. $1$
• C. $70$
• D. $196$

Answer 1

The correct option is A $0$

$\Rightarrow 5T_5=9T_9.$ $T_n=a+(n-1)d$ . for A.P. a be the first term of A.P & d be the common difference

$\Rightarrow 5(a+(5-1\left)d\right)=9(a+(9-1\left)d\right)$

$\Rightarrow 5a+20d=9a+72d.$

$\Rightarrow 4a=-52d.$

$\Rightarrow a=-13d.$

$\Rightarrow a+13d=0.$

$T_{14}=a+(14-1)d.$

$=a+13d.$

$=0$