Is 0 a term of the A.P. 31,28, 25,…? Justify your answer. - Vidyadip

Question

Is 0 a term of the A.P. 31,28, 25,…? Justify your answer.

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Answer

A.P. $31,28,25, \ldots$
Here, $a=31, d=28-31=-3$
Let 0 be the nth term, then
$
\begin{aligned}
& T_n=a+(n-1) d \\
& 0=31+(n-1)(-3) \\
& 0=31-3 n+3 \\
& \Rightarrow 3 n=34 \\
& n=\frac{34}{3} \\
& =11 \frac{1}{3}
\end{aligned}
$
Hence 0 is not any term of the A.P.

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