Question

Which term of an AP $21,18,15,...$. is zero?

Answer 1

Given:

The A.P is $21,18,15,\dots ,0,\dots .$

The first term $\left(a\right)$ is $21$

The Common difference$\left(d\right)$ is$-3$
Let ${\mathrm{n}}^{\text{th}}$ term be zero.
Now find the value of $n$.
$$\begin{gathered} n^{\text{th}}\text{term}=a+(n-1)d \\ \Rightarrow 0=21+(n-1)(-3) \\ \Rightarrow 3(n-1)=21 \\ \Rightarrow n-1=7 \\ \Rightarrow n=8 \end{gathered}$$
Hence, the eighth term for the given Arithmetic Progression is zero.