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

Sum

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

#### Solution

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, tn = 996

Since tn = a + (n – 1)d,

996 = 100 + (n – 1)(4)

∴ 996 = 100 + 4n – 4

∴ 996 = 96 + 4n

∴ 996 – 96 = 4n

∴ 4n = 900

∴ n = 900/4 = 225

Now, Sn = "n"/2 ("t"_1 + "t"_"n")

∴ S225 = 225/2 (100 + 996)

= 225/2 (1096)

= 225 × 548

= 123300

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

Concept: Sum of First n Terms of an AP
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