Question

Which term of A.P. $121,117,\mathrm{113...}$ is its first negative term? If it is the $nth$ term, find $S_n$

Answer 1

AP $121,117,1131$

$\Rightarrow a=121$

$d=-4$

$m=121+(n-1)-4<0$

$121-4n+4<0$

$-4n+125<0$

$4n>125<0$

$4n>125\Rightarrow m>\frac{125}{4}=31.25$

first negative term $\Rightarrow {32}^{th}$

$\Rightarrow n^{th}term=121+31\times 4\to 121-124=-3$

Sum $n^{th}$ term $=16[121-3]=16\times \left[118\right]$

$=1188$