Question

Which term of an $A.P$. $150,147,144$ is its first negative term ?

Answer 1

$150,147,144$

$a_2-a_1=147-150$

$d=-3$

$a_3-a_2=144-147=-3$

$\therefore a_1=150;d=-3$

as this A.P converges to O and the next term will be -3

so, $a_n=a+(n-1)d$

$\Rightarrow -3=150+(n-1)-3$

$-3-150=(n-1)-3$

$-153=(n-1)-3$

$\frac{-153}{-3}=(n-1)$

$51=n-1$, so $n=52$

$\therefore {52}^{th}$ term is the $1^{st}$ negative term of given A.P