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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Sequences and Series

NDA 2023 · Mathematics · Sequences and Series

The first and the second terms of an AP are (5)/(2) and (23)/(12)...

The first and the second terms of an AP are 52\frac{5}{2} and 2312\frac{23}{12} respectively. If nth n^{\text{th }} terms is the largest negative term, what is the value of nn ?

Options

  1. A55
  2. B66
  3. C77
  4. Dnn cannot be determined

Correct answer

B. 66

Step-by-step solution

a=52a+d=2312∴d=2312−52=−712a=\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 APA P. i.e. Tn<0⇒a+(n−1)d<052+(n−1)(−712)<030−7(n−1)<0⇒30−7n+7<07n>37⇒n>377\quad T n < 0 \Rightarrow a+(n-1) d < 0\frac{5}{2}+(n-1)\left(-\frac{7}{12}\right) < 030-7(n-1) < 0 \Rightarrow 30-7 n+7 < 07 n > 37 \Rightarrow n > \frac{37}{7} For integer value, n=6n=6.
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