Question

Which term of the AP 150,147,144,.....Is its first negative term ?

Answer 1

AP is 150, 147, 144 …
a = 150
d = -3
Tn < 0
Tn < 0
a+(n-1)d < 0
150+(n-1)-3<0
-150 > (n-1) (-3)
50 < n-1
51 < n.
So,
$T_{51}=150+(51-1)(-3)$
=150+(-150)
=0
So, $T_{52}$ is the first negative number
$T_{52}=\frac{150+5}{x-3}$
= -3.