Question

If $100$ times the ${100}^{th}$ term of an $A.P.$ with non zero common difference equals the $50$ times its ${50}^{th}$ term, then the ${150}^{th}$ term of this $A.P.$

• A. $150$
• B. $150$ times its ${50}^{th}$ term
• C. Zero
• D. $-150$

Answer 1

The correct option is C Zero

Let the first term of the $A.P.$ is $a$ and common difference is $d$
$T_n=a+(n-1)d$
Therefore,
$T_{100}=a+99d$ and $T_{50}=a+49d$
From the given problem statement, we have
$100(a+99d)=50(a+49d)$
$\Rightarrow 2a+198d=a+49d$
$\Rightarrow a+149d=0$
$\therefore T_{150}=a+149d=0$