Question

which term of the AP 108,103,98,... is ots first negative term?

Answer 1

Let a be the first term

Let d=common difference

Given a=108

d=103-108

=-5

Let the nth term be the first negative term

So

a+(n-1)d<0

108-5(n-1)<0

108-5n+5<0

5n>113

The least value of n is 23 for which

23*5=115>113

So the 23rd term is the first negative.

a+22d

=108-22*5

=108-110=-2

-2 is the first negative term.

Hope it helps.

Answer 2

a=108
d=a2-a
d=103-108
d=-5

a23=a+22d
a23=108+22(-5)
a23=108-110
therefore,a23=-2.

Thus,-2 is the first -ve term.
{Its very short and simplified answer.}
{Hope it'll help you.}
{Thanks.}