Question

In the natural numbers from 10 to 250, how many are divisible by 4?

Answer 1

The least positive natural number from 10 to 250 divisible by 4 is 12.
The sequence divisible by 4 is 12, 16, 20, .... , 248.
Now,

\[t_n = a + \left( n - 1 \right)d\]

\[ \Rightarrow 248 = 12 + \left( n - 1 \right)\left( 4 \right)\]

\[ \Rightarrow 248 = 12 + 4n - 4\]

\[ \Rightarrow 248 = 8 + 4n\]

\[ \Rightarrow 248 - 8 = 4n\]

\[ \Rightarrow 4n = 240\]

\[ \Rightarrow n = 60\]

Hence, 60 numbers are divisible by 4.