Question

Which term of AP 121, 117, 113,.... is its first negative term?​

Answer 1

Step-by-step explanation:

$\huge \underline{Answer - }$

$</p><p> \bold{Given -}</p><p> \\ </p><p>AP = 121 , 117 , 113 , ............</p><p> \\ \\ </p><p> \bold{To \:Find -}</p><p> \\ </p><p>First \: Negative \: Term </p><p> \\ \\ </p><p> \bold{a = 121}</p><p> \\ </p><p> \bold{d = 117 - 121 = - 4}</p><p> \\ \\ </p><p>For \: {n}^{th} \: term \: of \: the \: AP - </p><p> \\ \\ </p><p> \bold{a_{n} = a + (n-1)d} \\ </p><p> \leadsto121 + (n-1)-4 \\ </p><p> \leadsto 121 + (-4n+4) \\ </p><p> \leadsto121 - 4n + 4 \\ </p><p> \leadsto \fbox \bold{ a_{n} = 125 - 4n}</p><p> \\ </p><p>Now, \\ </p><p>For \: First \: negative \: term </p><p> \\ </p><p> \bold{a_{n} < 0} \\ </p><p>It \: means, \\ </p><p>125 - 4n < 0 \\ </p><p>125 < 4n \\ </p><p>4n > 125 \\ </p><p>n > \frac{125}{4} \\ </p><p> \fbox \bold{n > 31.25}</p><p></p><p> \\ \\ </p><p>Hence, </p><p> \\ </p><p> \bold{32 {}^{nd} } \: term \: \: of \: the \: AP \: is \: First \: Negative \: Term$

Answer 2

Answer:

Refers to the attachment