7. How many three digit natural numbers are divisible by 4 ?
Sol. The three digit natural numbers that are divisible by 4 are : 100, 104, 108, ........ 996.
It is an A.P. with a = t1 = 100, d = 4
Let, tn = 996
We know that for an A.P.
tn = a + (n – 1) d
∴ 996 = 100 + (n – 1) 4
∴ 996 = 100 + 4n – 4
∴ 996 = 96 + 4n
∴ 4n = 996 – 96
∴ 4n = 900
∴ n = 900/4
∴ n = 225
∴ There are 225 three digit natural numbers that are divisible by 4.
