One of the most important question from arithmetic progression chapter in which we have been given a series of AP 20, 19 1/2, 18 1/2, 17 3/4 and we have to find its first negative term?
Book RS Aggarwal, Class 10, Arithmetic Progression, chapter 5A, question no 25.
20,19 1/4​, 18 1/2​,....
or 20,77​/4,37/2​,....
a=20
d=77​/4−20=−3/4​
Let nth term of A.P. be first negative term
So, 20+(n−1)(4−3​)<0
⇒80−3n+3<0
⇒3n>83
⇒n>27 2/3​
Hence, 28th term is first negative term.