Question

Which term of the A.P. 21, 42, 63, 84, ... is 210?
(a) 9^th
(b) 10^th
(c) 11^th
(d) 12^th

Answer 1

The given A.P. is: 21, 42, 63, 84, ...

First term = a = 21
Common difference = d = 42 – 21
= 21
n^th term = a_n = 210

Now,
$$\begin{gathered} a_n=a+\left(n-1\right)d \\ \Rightarrow 210=21+\left(n-1\right)\left(21\right) \\ \Rightarrow 210=21+21n-21 \\ \Rightarrow 210=21n \\ \Rightarrow n=10 \end{gathered}$$

Therefore, the 10^th term of the A.P. 21, 42, 63, 84, ... is 210.

​Hence, the correct option is (b).