Question

If $5$ times the $5^{th}$ term of an A.P is the same as $7$ time the $7^{th}$ term, then find its ${12}^{th}$ terms.

• A. $0$
• B. $11$
• C. $14$
• D. $18$

Answer 1

Answer: (A)

$0$

$t_5=a+4d$ and $t_7=a+6d$
Now $5t_5=7t_7$
$\Rightarrow 5(a+4d)=7(a+6d)$
$\Rightarrow a+11d=0$
$t_{12}=a+11d=0$