Question

Find whether $0$ is a term of the A.P. $40,37,34,\mathrm{31...}$

Answer 1

Let $a=$ first term of A.P., $d=$ common difference $n^{th}$ term, $a_n=a+(n-1)d$;

To find n for $a_n=0$

$\Rightarrow a+(n-1)d=0$

Here $a=40,d=37-40=-3$

$\Rightarrow 40-3(n-1)=0$

$\Rightarrow 40=3(n-1)$

$\Rightarrow 40=3n-3$

$\Rightarrow 3n=43$

$\Rightarrow n=\frac{43}{3}$ not an integer $\Rightarrow 0$ not a term in A.P.