Question

Is $0$ a term of the AP$31,28,25,\dots ?$ Justify your answer.

Answer 1

Find if $0$ is term in $31,28,25....$or not

If we assume $0$ be the $n^{th}$ term of given AP such that $a_n$ = $0$.

$a=31=$First term

$$\begin{gathered} \text{common difference} \\ d=28–31 \\ =–3 \end{gathered}$$

The $n^{th}$ term of an AP, is

${\mathbf{a}}_{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{a}\mathbf{}\mathbf{+}\mathbf{}\mathbf{(}\mathbf{n}\mathbf{}\mathbf{-}\mathbf{}\mathbf{1}\mathbf{)}\mathbf{d}$

$\Rightarrow 0=31+(n-1)(-3)$

$\Rightarrow \mathrm{n}=\frac{34}{3}$

Upon solving we do not obtain an integer value for $n$.

Hence, $0$ is not a term of the given AP.