Choose the correct answer from the given four options:
Which term of the AP: $ 21,42,63,84, \ldots $ is 210 ?
(A) $ 9^{\mathrm{th}} $
(B) $ 10^{\text {th }} $
(C) $ 11^{\text {th }} $
(D) $ 12^{\text {th }} $

Given:

Given A.P. is \( 21,42,63,84, \ldots \)

To do:

We have to find $210$ is which term of the given A.P.

Solution:

Let $210$ be the $n$th term of the given A.P.

Here,

$a_1=21, a_2=42, a_3=63$

Common difference $d=a_2-a_1=42-21=21$

We know that,

nth term $a_n=a+(n-1)d$

Therefore,

$a_{n}=21+(n-1)(21)$

$210=21+n(21)-1(21)$

$210-21=21n-21$

$210=21n$

$n=\frac{210}{21}$

$n=10$

Hence, $210$ is the 10th term of the given A.P.