Question

find the sum of integers between 100 and 200 that are divisible by 3 and 7.​

Answer 1

Numbers which are divisible by 3 are 102,105,108......................198

Total numbers 198=102+(x-1)3

198-102=(x-1)3

96=(x-1)3

x-1=32

x=33

Sum of these numbers

=33/2[2(102)+(33-1)3]

=33/2[204+96]

=33/2(300)

4940

Numbers which are divisible by 7 are 105,112,119.......................196

Total numbers 196=105+(x-1)7

x=14

Sum of these numbers

=14/2[2(105)+(14-1)7

=2107

Numbers which are divisible by 21 are 105,126,147....................189

Sum of these numbers=735

Sum of integers which are divisible by 3 and 7= 4940+2107-735

ANSWER=6312