Question

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

Answer 1

All three-digit numbers which are divisible by 13 are 104, 117, 130, 143,...... 938.

This is an AP in which a = 104, d = (117 – 104) = 13 and l = 938

Let the number of terms be n

Then T_n = 938

⇒ a + (n – 1)d = 988

⇒ 104 + (n – 1) × 13 = 988

⇒ 13n = 897

⇒ n = 69

∴ Required sum = `n/2 (a + l)`

= `69/2 [104 + 988]`

= 69 × 546

= 37674

Hence, the required sum is 37674.