Question

which term of an sequence 168, 163, 158.... is first negative term

Answer 1

to the common difference(d) is 163 - 168 = - 5 

so the first term (a) = 168 

so using formula for n th term we have

 let n be the number if terms

$a_n=a+(n-1)d$

so since the term is negative so  $a_n<0$

$a+(n-1)d<0$

putting the values 

⇒ 168 + (n - 1)(-5) < 0
⇒ 168 - 5n + 5 < 0 
⇒ 5n > 173 
⇒ n > 34.6

so since n can't be fraction so the first negative term is 35 ANSWER

Answer 2

Given :-
First term(a) = 168
Common difference(d) = 163 - 168 = - 5 

Now An = a + (n - 1 ) d

Since the term is negative so  




168 + (n - 1)(-5) < 0
168 - 5n + 5 < 0 
5n > 173 
n > 34.6
So the first negative term will be 35th term.