Question

Which term of the AP45,41,37.... is the first negative term

Answer 1

There is a sequence in which 4 is continuously decreasing.then


37,33,29,25,21,17,13,9,5,1,-3

-3 is the first negative term


I hope this much will help

Answer 2

45,41,37,................. is an A.P
here....
a=45

d=t2-t1=41-45=-4
d=-4
we have to find the first n for which nth term is negative.
here,
tn<0.......................(1)

we know that,
tn=a+(n-1)d....................(2)

from(1) &(2)
a+(n-1)d<0
45+(n-1)-4<0
45-4n+4<0
49-4n<0
49<4n
49/4<n
12.25<n
$n = > 13$
we know that,

tn=a+(n-1)d

tn=45+(13-1)-4

tn=45+12*-4

tn=45-48

tn=-3

the first term which is negative is -3.

I think this is very formal and a systematic way .

$hope \: this \: helps$