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.