Question

Which term of A.P.: $21,42,63,84,...$is 210?

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

Answer 1

The correct option is B

${10}^{\mathrm{th}}$

Finding the value of $n$:

The $n^{\mathrm{th}}$ term of an A.P. can be found by using the formula given below:

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

Here, $a$ is the first term of the sequence and $d$ is the common difference.

Let the $n^{\mathrm{th}}$ term of A.P. be 210.

It is given that $a=21,T_n=210\mathrm{and}d$ can be found as follows:

$\begin{array}{rcl}\therefore d& =& T_2-T_1\\ & =& 42-21\\ & =& 21\end{array}$

Substituting the known values in (1):

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

Therefore, the ${10}^{\mathrm{th}}$ term of the given A.P. is 210.

Final Answer:

Hence, option B is correct.