Question

Check if $0$ is a term of the AP: $31,28,25,$_____

Answer 1

If possible let $0$ is the $n$ th term of the given series. Where $n$ is a natural number.

Then

$31+(n-1)(-3)=0$ [ Since the first term of the series is $31$ and common difference is $-3$]

or, $3(n-1)=31$

or, $n=\frac{31}{3}+1$

This contradicts to the fact $n$ is natural number.

So $0$ does not belong to the series.