Question

Which term of the ap :121,117,113,......isits first negative term?

Answer 1

Let Tn =0
a+(n-1)d=0
121+(n-1)(-4)=0
121-4n+4=0
125-4n=0
-4n=-125

n=125/4
but terms can't be in fraction.
[ suppose n= 9,then Tn =0,then 10th term of AP WILL BE NEGATIVE.TAKE ANOTHER QUESTION OF THIS TYPE.]

Answer 2

a = 121

d = -4

let an= 0

then

an = a + (n-1)d

=> 0 = 121 + (n-1)(-4)

=> 0 = 121 - 4n + 4

=> 4n = 125

=> n = 125/4

=> n = 31.25

as n must be natural number then n= 32

32nd term is First negative number.

a32 = 121 + (31)-4

= 121 - 124 = -3