Question

Which term of the AP: $21,42,63,84\dots$ is $210$?

• A. $9\mathrm{th}$
• B. $10\mathrm{th}$
• C. $11\mathrm{th}$
• D. $12\mathrm{th}$

Answer 1

The correct option is B

$10\mathrm{th}$

Step 1. Explanation for the correct option.

The given A.P. is $21,42,63,84\dots$

Here, first term, $a=21$

common difference,

$$\begin{gathered} d=42-21 \\ =21 \end{gathered}$$

$n\mathrm{th}$ term, $a_n=210$

The $n\mathrm{th}$ term of an A.P. is given by the formula,

$a_n=a+\left(n-1\right)d$

Substitute the given values in the above formula:

$$\begin{gathered} 210=21+\left(n-1\right)21 \\ \Rightarrow 210-21=21\left(n-1\right) \\ \Rightarrow 189=21\left(n-1\right) \\ \Rightarrow \frac{189}{21}=\left(n-1\right) \\ \Rightarrow 9=\left(n-1\right) \\ \Rightarrow n=9+1 \\ \therefore n=10 \end{gathered}$$

So, the $10\mathrm{th}$ term of an A.P. is $210$.

Step 2. Explanation for the incorrect options.

Since, the $10\mathrm{th}$ term of an A.P. is $210$. So, all the other options are incorrect.

Hence, the correct option is $\mathrm{B}$.