Question

find the sum of all integers from 1 to 200 excluding those that are multiples of 3 or 7
(Ls arithematic progression)​

Answer 1

Answer:

The sum of all integers from 1 to 200 which are not multiples of 3 or 7

step 1

the sum of all integers from 1 to 200 = n x (n+1) / 2

                                                          = 200 x 201 /2

                                                          = 20100

step 2

the sum of all integers which are multiples of 3 between 1 to 200

   = 3+6+9+12+..................+198

   = 3 (1+2+3+4+................+ 66)

   =  3 (66 x 67)/2

   =  3 x 2211 = 6633

step 3

the sum of all integers which are multiples of 7 between 1 and 200

   = 7+14+21+28+...............+196

   = 7(1+2+3+4+...................+28)

   = 7(28 x 29)/2

   = 7 x 406 = 2842

the multiples of 3 and 7 = 6633 + 2842 =9475

 

step 4

so, solution = 20100 - 9475 = 10625