How many numbers lie between 10 and 300,

Here, the first number is 11, which divided by 4 leave remainder 3 between 10 and 300. Last term before 300 is 299, which divided by 4 leave

remainder 3.

∴                                                         11,15,19,23…. 299

Here, first term (a) = 11, common difference d = 15 -11 = 4

$\because \quad$ nth term, $a_{n}=a+(n-1) d=l \quad$ [last term]

$\Rightarrow \quad 299=11+(n-1) 4$

$\Rightarrow \quad 4(n-1)=288$

$\Rightarrow \quad(n-1)=72$

$\therefore \quad n=73$