Question

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

Answer 1

The given A.P is 11, 15, 19, .....,299.
$$\begin{gathered} a=11 \\ d=4 \\ {a}_n=299 \\ \Rightarrow a+\left(n-1\right)d=299 \\ \Rightarrow 11+\left(n-1\right)4=299 \\ \Rightarrow \left(n-1\right)4=288 \\ \Rightarrow n=73 \end{gathered}$$