Question

Question 18
How many numbers lie between 10 and 300, which divided by 4 leave a remainder 3?

Answer 1

Here, the first number is 11, which when divided by 4 leave remainder 3 between 10 and 300. Last term before 300 is 299, which when divided by 4 leave remainder 3.
$\therefore$ nth term, $a_n$ = a + (n - 1)d = 299
$\Rightarrow$ 299 = 11 + (n - 1)4
$\Rightarrow$ 299 - 11 = (n - 1)4
$\Rightarrow$ 4(n - 1) = 288
$\Rightarrow$ (n - 1) = 72
$\therefore$ n = 73