Find sum of integers from 1 to 100 that are divisible by 2 or 5.

Let =  Sum of all the numbers from 1 to 100 which are divisible by 2.
  =  Sum of all the numbers from 1 to 100 which are divisible by 5.
=  Sum of all numbers from 1 to 100 which are divisible by both 2 and 5.

∴           Required Sum =                                                      ...(i)
Now,                    
Here,                       
         a + (n - 1)d = 1800    2 + (n - 1)2 = 100
or                (n - 1)2 = 98        or       n - 1 =    or  n = 50

∴                        
                          
Here, a = 5, d = 5,
         a + (n - 1)d = 100       or      5 + (n - 1)5 = 100
            n - 1 = 19    n = 20

∴                
                
∴  from (i), we have
           Required sum = 2550 + 1050 - 550 = 3050.