Question

Which term of ap 121,171 ,113 is the first negative term?

Answer 1

Given AP is:

121, 117, 113, ................

First term a = 121

Common difference d = 117-121 = -4

Let nth term is the first negative term in AP

Now nth tern in AP = a + (n-1)*d

                              = 121 + (n - 1)*(-4)

                              = 121 - 4n + 4

                              = 125 - 4n

Now, we have to find the suitable value of n so that the value of (125 - 4n) is negative.

=> 125 - 4n < 0

=> 125 < 4n

=> 4n > 125

=> n > 125/4

=> n > 31.25

Since the term can not be in decimal form (term is always taken a positive integer) 

So, n = 32 

Now, by taking value of n = 32, we get

nth term  = 125 - 4*32

              = 125 - 128

              = -3

This is the first negative term in the series.

So, n = 32


plz mark brainliest

Answer 2

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

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

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

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

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

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

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

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

$\bf\huge = 125 < 4n$

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

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

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

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

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