 Hi and welcome to the session. Let us solve the following question which says, find the sum of all the numbers between 200 and 400 which are divisible by 7. Let us now begin with the solution and the numbers divisible by 7 which are between 200 and 400. The smallest number is 203 then we have 210, 217, 224 and the last number is 399. So this is an A B series. Now the first number which is divisible by 7 that is the first term is 203 and the common difference between the terms of this A B is 7 and the common difference that is denoted by T. Now the last term of the A B which is denoted by A N is equal to 399 and A N is equal to A plus N minus 1 into D where A is the first term, D is the common difference and N is the number of terms which are divisible by 7 and between 200 and 400. So first we will try to find the value of N. Now A N is 399 is equal to 203 plus N minus 1 into D is 7. So this further gives 399 minus 203 is equal to N minus 1 into 7. Now on subtracted 203 from 399 we get 196 which is equal to N minus 1 into 7 or we can say that N minus 1 is equal to 196 upon 7 which is equal to 28 or N is equal to 28 plus 1 which is equal to 29. Therefore there are 29 numbers between 200 and 400 which are divisible by 7. Now we have to find the sum of these 29 numbers. So this is equal to 28 upon 2 into A, A is 203 plus N minus 1 that is 29 minus 1 into 7. Since the formula to find the sum of N numbers is N upon 2 into 2A plus N minus 1 into D where N is the number of terms A is the first term and D is the common difference. By using this formula we have S 29 is equal to 29 upon 2 into 203 plus 29 minus 1 into 7. So this is further equal to 29 upon 2. Now simplifying this bracket we have 406 plus 28 into 7 which is further equal to 29 upon 2 into 28 into 7 as 196 which is further equal to 29 upon 2. Now adding 406 where 196 gives 602. So this is further equal to 29 into 602 upon 2 2 into 301 is 602 so we have 29 into 301 which is further equal to 8729. Therefore our answer is the sum of numbers which are divisible by 7 between 200 and 400 is 8729. So this completes the solution take care and have a good day.