The sum of all numbers that are divisible by 3 from 11 to 1000 is …�

1.	The sum of all numbers that are divisible by 3 from 11 to 1000 is ……………… A) 766155 B) 766118 C) 166815 D) 766815
Answer» Correct option is (C) 166815 Numbers from 11 to 1000 which are divisible by 3 are 12, 15, 18, ..... , 999. \(\therefore\) Sum = 12+15+18+...+999 = (3+6+9+12+15+...+999) - (3+6+9) = 3 (1+2+3+...+333) - 18 \(=3\times\frac{333\times334}2-18\) \(=3\times333\times167-18\) = 166833 - 18 = 166815 Correct option is C) 166815

The sum of all numbers that are divisible by 3 from 11 to 1000 is ……………… A) 766155 B) 766118 C) 166815 D) 766815

Answer»

Correct option is (C) 166815

Numbers from 11 to 1000 which are divisible by 3 are 12, 15, 18, ..... , 999.

\(\therefore\) Sum = 12+15+18+...+999

= (3+6+9+12+15+...+999) - (3+6+9)

= 3 (1+2+3+...+333) - 18

\(=3\times\frac{333\times334}2-18\)

\(=3\times333\times167-18\)

= 166833 - 18

= 166815

Correct option is C) 166815