Question

Find the sum of three-digit natural numbers, which are divisible by 4.

Answer 1

The three-digit natural numbers divisible by 4 are

100, 104, 108, ......, 996

The above sequence is an A.P.

∴ a = 100, d = 104 – 100 = 4

Let the number of terms in the A.P. be n.

Then, t_n = 996

Since t_n = a + (n – 1)d,

996 = 100 + (n – 1)(4)

∴ 996 = 100 + 4n – 4

∴ 996 = 96 + 4n

∴ 996 – 96 = 4n

∴ 4n = 900

∴ n = `900/4`

∴ n = 225

Now, `S_n = n/2 (t_1 + t_n)`

∴ `S_225 = 225/2 (100 + 996)`

= `225/2 (1096)`

= 225 × 548

= 123300

∴ The sum of three-digit natural numbers, which are divisible by 4 is 123300.