Question

If $100$ times the ${100}^{th}$ term of an A.P. is equal to the $50$ times the ${50}^{th}$ term, then the value of ${150}^{th}$ term of this A.P. is

• A. $0$
• B. $150$
• C. $50$
• D. dependent on the value of the first term.

Answer 1

The correct option is A $0$

Given: $100\times [a+(100-1\left)d\right]=50\times [a+(50-1\left)d\right]$
$\Rightarrow 2a+198d=a+49d\Rightarrow a+149d=0\therefore T_{150}=0$