Question

which term of AP. 121,117,113,........, is its first negative term. ? please explain

Answer 1

Let the first negative term of the given A.P = - x
In this A.P
First term (a) = 121
Common difference = - 4

Let the first negative be the last term of the A.P
Therefore
Last term < 0
a + (n - 1)d < 0
121 + (n - 1) - 4 < 0
121 - 4n + 4 < 0
125 < 4n
125/4 < n
n > 31.25

So, number of terms is greater than 31.25
The nearest number to 31.25 is 32.

So, the 32nd term is the first negative term.

Hope you understand my answer.