Question

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

• A. $-150$
• B. $150$ times its ${50}^{th}$ term
• C. $150$
• D. $0$

Answer 1

Answer: (D)

$0$

Let say $a$ be the first term and $d$ be the common difference of the AP.

Given: $100(a+99d)=50(a+49d)$ [using $n^{th}$ term $a_n=a+(n-1)d$]

$\Rightarrow 2a+198d=a+49d$

$\Rightarrow a+149d=0$

Also, $T_{150}=a+149d=0$

Hence, the option 'D' is correct.