Question

Which term of the AP 121,117,113,.......is the first negative

Answer 1

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

$a=121$

$d=117-121=-4$

Let $a_n=0$

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

$\Rightarrow$ $0=121+(n-1)-4$

$\Rightarrow$ $0=121-4n+4$

$\Rightarrow$ $4n=125$

$\Rightarrow$ $n=\frac{125}{4}$

$\Rightarrow$ $n=31.25$

$n$ must be a natural number.

$\therefore$ $n=32$

${32}^{nd}$ term is the first negative number.

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

$\Rightarrow$ $a_{32}=121+(32-1)(-4)$

$\Rightarrow$ $a_{32}=121+\left(31\right)(-4)$

$\Rightarrow$ $a_{32}=121-124$

$\Rightarrow$ $a_{32}=-3$