Question

find the sum of all integers from 100 to 400, which are divisible by either 3 or 4.Also find integers which are divisible by neither 3 nor 4

Answer 1

Answer:

37750

37500

Step-by-step explanation:

100  to 400

Divisible by 3  are

102  , 105 ,....................................................................................., 399

Sum

= 3 * ( 34  + 35 +........................................................................+ 133)

= 3 * (100/2)(34 + 133)

= 25050

Divisible by 4  are

100  , 104 ,....................................................................................., 400

Sum

= 4 * ( 25 + 26 +........................................................................+ 100)

= 4 * (76/2)(25 + 100)

= 19000

but these have repeated number divisible by 12

108 , 120 ,................................................................., 396

Sum

= 12 * (9 + 10 +........................................................+ 33)

= 12 * (25/2)(9 + 33)

= 6300

the sum of all integers from 100 to 400, which are divisible by either 3 or 4

= 25050 + 19000 - 6300

= 37750

Sum of integers which are divisble by neither 3 nor 4

= Total Sum -   37750

= 100 + 101 +.......................................................+ 400 -  37750

= (301/2)(100 + 400) - 37750

= 75250 - 37750

= 37500