Advertisement Remove all ads

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

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Sum

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

Advertisement Remove all ads

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
  Is there an error in this question or solution?
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×