 Hello and welcome to the session. I am Asha and I am going to help you with the following question that says, find the sum of integers from 1 to 100 that are divisible by 2 or 5. Let us now start with the solution. First let us write the integers from 1 to 100 which are divisible by 2. First is 2 and we have 4, 6, 8, 10 and so on up to 98 and 100. So the first term is 2 and let us denote it by small a and the common difference is again 2 and let us denote it by small d. Now the last term of the sequence which is a n is equal to 100. The formula of a n is a plus n minus 1 into d is equal to 100 where n is equal to number of terms from 1 to 100 which are divisible by 2. Now a is 2 plus n minus 1 into 2 is equal to 100. So that implies n minus 1 into 2 is equal to 98 or n minus 1 is equal to 49 or n is equal to 50. So the number of terms from 1 to 100 which are divisible by 2 are 50. Now let us find the sum of these 50 terms. So first let us write down the formula to find the sum of n terms. So this is equal to n upon 2 into 2a plus n minus 1 into d. So s50 will be equal to 50 upon 2 into 2 into 2 plus 50 minus 1 into 2 which further gives 25 into 4 plus on simplifying we have 49 into 2. This is equal to 98 which is further equal to 25 into 102. So this is equal to 2550 and therefore the sum of integers from 1 to 100 which are divisible by 2 to 550. Now let us find the sum of integers from 1 to 100 which are divisible by 5 but not by 2. So the integers from 1 to 100 which are divisible by 5 but not by 2, 5, 15, 25 and so on up to 95. The term of this sequence which is capital A is equal to 5 and the common difference by capital D is equal to 10 and the last term is denoted by an is equal to 95 and its formula is a plus n minus 1 into d is equal to 95 where n is the number of terms from 1 to 100 which are divisible by 5 but not by 2. So a is 5 plus n minus 1 d is 10 so this is equal to 95 or n minus 1 into 10 is equal to 90. So this implies n minus 1 is equal to 9 or n is equal to 10. So the number of terms from 1 to 100 which are divisible by 5 but not by 2 are 10. So let us now find the sum of these 10 terms. So we have 10 upon 2 into 2 into a is 5 plus n minus 1, 10 minus 1 into d and d is 10. So this is equal to 5 into 10 plus 90 so this is equal to 5 into 100 which is equal to 500. Therefore sum of integers 1 to 100 which are divisible by 5 but not by 2 are 500 and therefore our answer is sum of integers from 1 to 100 which are divisible by 2 or 5 to 550 plus 500 this is the sum of integers which are divisible by 2 and this is the sum of integers which are divisible by 5 but not by 2 and which are between 1 and 100. So this is equal to 3050 so this is the sum of integers which are divisible by 2 or 5 from 1 to 100. So this completes the solution take care and have a good day.