Question

which term of the A.P. $100,97,94,91,...$ is its first negative term?

Answer 1

$\begin{array}{c}A.P100,97,94,\mathrm{91...............}\\ a=100d=-3\end{array}$

let first negative term be $-1$

$\begin{array}{c}-1=a+\left(n-1\right)d\\ \Rightarrow -1=100+\left(n-1\right)-3\\ \Rightarrow -1=100-3n+3\\ \Rightarrow -3n=-1-100-3\\ =3n=104\\ n=34.6\end{array}$

let second term be $-2$

$\begin{array}{c}-2=a+\left(n-1\right)d\\ \Rightarrow -2=100-3n+3\\ \Rightarrow -3n=-100-3-2\\ =-3n=-105\\ n=35\end{array}$