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 $A.P.$ is :

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

Answer 1

Answer: (D)

zero

Answer 2

$100 (a + 99d) = 50 (a + 49d)$ $2a + 198 d = a + 49d$ $a + 149d = 0$ $T_{150} = a + 149 d = 0$