Question

which term of the AP : 121 117 113 ... is first negative term?

Answer 1

The general term or nth term of A.P is given by an = a + (n – 1)d,
where a is the first term, d is the common difference and n is the number of term.

Solution:-
Given:first term(a)= 121 
common difference (d)= 117- 121 = -4
∵ n th term of an AP

an = a + (n – 1)d
⇒121+(n-1) ×(-4)
⇒121-4n+4
⇒12+4-4n
⇒125 -4n
an= 125 -4n

For first negative term , an <0
⇒ 125-4n<0
⇒125<4n
⇒4n>125
⇒n>125/4
⇒n> 31 1/4

least integral value of n= 32

Hence, 32nd term of the given AP is the first negative term. 
May this helps thn mrk as brainliest.

Answer 2

$\bf\huge\boxed{\boxed{\bf\huge\:Hello\:Mate}}}$

$\bf\huge AP = 121 , 117 \:and\: 113$

$\bf\huge a = 121 , d => 117 - 121 = -4$

$\bf\huge => a_{n} = a + (n - 1)d$

$\bf\huge => 121 - 4n + 4 = 125 - 4n$

$\bf\huge First\: Negative\: Term$

$\bf\huge = a_{n} < 0$

$\bf\huge = 125 - 4 < 0$

$\bf\huge = 125 < 4n$

$\bf\huge = \frac{125}{4} < n$

$\bf\huge = 31 \frac{1}{4} <n$

$\bf\huge n \:is\: an\:integer\:and\:n >31 \frac{1}{4}$

$\bf\huge The\:first\:Negative\:Term\:=\:32nd\:term$

$\bf\huge\boxed{\boxed{\:Regards=\:Yash\:Raj}}}$