Q40 / 90 · JEE Main 2012 (Offline) · Mathematics

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

  • A
    $-150$
  • B
    $150$ times its $50^{\text {th }}$ term
  • C
    $150$
  • Correct answer
    D
    zero

Solution

$100\left(T_{100}\right)=50\left(T_{50}\right) \quad \Rightarrow 2[a+99 d]=a+49 d \Rightarrow a+149 d=0 \quad \Rightarrow T_{150}=0$

Hence, the correct answer is option: 'D'.

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