Write the value of n for which nth terms of the A.P.s 3, 10, 17,

For the first series, $a=3, d_{1}=7$

For the second series, $b=63, d_{2}=2$

Given:

$a_{n}=b_{n}$

$\Rightarrow a+(n-1) d_{1}=b+(n-1) d_{2}$

$\Rightarrow 3+(n-1) 7=63+(n-1) 2$

$\Rightarrow 3+7 n-7=63+2 n-2$

$\Rightarrow 5 n=65$

$\Rightarrow n=13$

Hence, the 13th terms of both the series are the same.