Question

Which term of the AP : 121, 117, 113, . . ., is the first negative term?
[Hint : Find n for an < 0]

Answer 1

$121 + (x - 1)( - 4) < 0 \\ 121 - 4x + 4 < 0 \\ 4x > 125 \\ x > 31.25 \\ first \: negative \: term \: is \: 32$

Answer 2

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

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

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

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

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

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

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

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

$\bf\huge = 125 < 4n$

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

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

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

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

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