Question

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

Answer 1

 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.