Question

Which term of the A.P: 201, 192, 183... is the first negative term.

Answer 1

$Given \:A.P : 201,192,183, \cdot\cdot\cdot$

$First \:term (a) = 201$

$Common \: differnce (d) \\= a_{3} - a_{2} \\= 183 - 192 \\= -9$

$\boxed { \pink { n^{th} \:term (a_{n}) = a + (n-1)d }}$

$Here, a_{n} < 0$

$\implies a + (n-1)d < 0$

$\implies 201 + (n-1)(-9) < 0$

$\implies (n-1)(-9) < - 201$

$\implies (n-1) < \frac{ - 201}{-9}$

$\implies n-1< \frac{ 67}{3}$

$\implies n< \frac{ 67}{3} + 1$

$\implies n< \frac{ 67+3}{3}$

$\implies n< \frac{ 70}{3}$

$\implies n< 23\frac{1}{3}$

$\therefore n = 23$

$\green { 23^{rd} \:term \: of \: is \: the \: first }\\\green { negative \: term }$

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