Question:
Which term of an AP : 21, 42, 63, 84,… is 210?
(a) 9th
(b) 10th
(c)11th
(d) 12th
Solution:
(b) Let nth term of the given AP be 210
Here, first term, $\quad a=21$
and common difference, $d=42-21=21$ and $a_{n}=210$
$\because$ $a_{n}=a+(n-1) d$
$\Rightarrow \quad 210=21+(n-1) 21$
$\Rightarrow \quad 210=21+21 n-21$
$\Rightarrow \quad 210=21 n \Rightarrow n=10$
Hence, the 10th term of an AP is 210.