Advertisement Remove all ads

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?

Advertisement Remove all ads

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.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

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

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×