Question

Which term of the AP
$20,19\frac{1}{4},18\frac{1}{2},17\frac{3}{4}$, …
will be the first negative term?

Answer 1

Given, AP:

$20,19\frac{1}{4},18\frac{1}{2},17\frac{3}{4}$

After simplification, we get,

$20,\frac{77}{4},\frac{37}{2},\frac{71}{4}$, ...

a = 20,

$d=\frac{77}{4}-20=-\frac{3}{4}$

Let the nth term be the first negative term.

$a_n$ = a + (n − 1)d < 0

∴$20+(n-1(-\frac{3}{4})<0$​​​​​​

∴ 80 − (n − 1)3 < 0

∴ 83 − 3n < 0

∴ 83 < 3n

∴ $\frac{83}{3}<n$

∴ $27\frac{2}{3}<n$

Hence, n = 28

Hence, the 28th term will be the first negative term of the given AP.