Q166 / 270 · NDA 2023 (Phase 1) · Mathematics

The first and the second terms of an AP are $\frac{5}{2}$ and $\frac{23}{12}$ respectively. If $n^{\text {th }}$ terms is the largest negative term, what is the value of $n$ ?

  • A
    $5$
  • Correct answer
    B
    $6$
  • C
    $7$
  • D
    $n$ cannot be determined

Solution

$a=\frac{5}{2}$ $a+d=\frac{23}{12}$ $\therefore \quad d=\frac{23}{12}-\frac{5}{2}=\frac{-7}{12}$ The largest negative term will be the first negative term as it is decreasing $A P$. i.e. $\quad T n \lt 0 \Rightarrow a+(n-1) d \lt 0$ $\frac{5}{2}+(n-1)\left(-\frac{7}{12}\right) \lt 0$ $30-7(n-1) \lt 0 \Rightarrow 30-7 n+7 \lt 0$ $7 n \gt 37 \Rightarrow n \gt \frac{37}{7}$ For integer value, $n=6$.

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

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