Question

Check $0$ is a term of an AP: $31,28,25,....$

Answer 1

Step 1. Find the common difference:

$$\begin{gathered} a_1=31 \\ {a}_2=28 \end{gathered}$$

$\begin{array}{rcl}& \Rightarrow & a_2-a_1=28-31\\ & =& -3\end{array}$

Step 2. Check $0$ is a term of an AP: $31,28,25,....$ by using the general term of AP:

We know that the general term of AP is $a_n=a+(n-1)d$.

$$\begin{gathered} \Rightarrow 31+(n-1)(-3)=0 \\ \Rightarrow 31-3n+3=0 \\ \Rightarrow 3n=34 \\ \Rightarrow n=\frac{34}{3} \end{gathered}$$

Thus, the value of $n$ is a fraction which is not possible.

Therefore, 0 is not a term for the given A.P.