Question

Find the sum of all three-digit natural numbers which are divisible by 13.

Answer 1

3-digit natural numbers: 100, 101, 102,……., 999.

3-digit natural numbers divisible by 13:

104, 117, 130,………, 988

Which is an AP.

Here, a = 104, d = 13, l = 988

l = a + (n – 1) d

988 = 104 + (n-1)13

n = 69

There are 69 terms.

Find the sum of 69 terms:

S_n = n/2(a + l)

= 69/2(104 + 988)

= 37674