Question

Find the first negative term oa the AP 121 '117 , 113

Answer 1

AP : 121,117,113,......
a=121
d=117-121= -4
If we need the first negative term, an needs to be less than 0.
i.e., an <0
a+(n-1)*d<0
121+(n-1)*-4<0
121-4n+4<0
125-4n<0
4n>125
n>31.25
Hence, the first negative term of the AP is 32nd term which will be -3.

Answer 2

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

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

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

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

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

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

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

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

$\bf\huge = 125 < 4n$

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

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

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

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

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