# Which Term of the Sequence 24, 23 1 4 , 22 1 2 , 21 3 4 ....... is the First Negative Term? - Mathematics

Which term of the sequence 24, $23\frac{1}{4,} 22\frac{1}{2,} 21\frac{3}{4}$....... is the first negative term?

#### Solution

24,

$23\frac{1}{4,}22\frac{1}{2,}21\frac{3}{4}$

This is an A.P.
Here, we have:
a = 24

$d = \left( 23\frac{1}{4} - 24 \right) = \left( - \frac{3}{4} \right)$

$\text { Let the first negative term be } a_n .$

$\text { Then, we have }:$

$a_n < 0$

$\Rightarrow a + \left( n - 1 \right) d < 0$

$\Rightarrow 24 + \left( n - 1 \right) \left( - \frac{3}{4} \right) < 0$

$\Rightarrow 24 - \frac{3n}{4} + \frac{3}{4} < 0$

$\Rightarrow 24 + \frac{3}{4} < \frac{3n}{4}$

$\Rightarrow \frac{99}{4} < \frac{3n}{4}$

$\Rightarrow 99 < 3n$

$\Rightarrow n > 33$

Thus, the 34th term is the first negative term of the given A.P.

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Exercise 19.2 | Q 5.1 | Page 12