 Hello and welcome to the session. Let us understand the following problem today. Find the sum given below 7 plus 10 1 by 2 plus 14 so on till 84. Now let us first discuss the formula for the sum. Let us term a n is represented as a plus n minus 1 d where a is equal to first term d is equal to common difference and n is equal to number of terms and sum is given by n by 2 multiplied by a plus a n where a n is the nth term. Now this is the key idea to our problem. Now let us write the solution. Given a p is 7 plus 10 1 by 2 plus 14 so on till 84. Now here a is equal to 7 d is equal to 10 1 by 2 minus 7 which is equal to 21 by 2 minus 7 which is equal to 7 by 2 a n that is the nth term is equal to 84. Now by key idea we have a n is equal to a plus n minus 1 d a n is given to us 84 which is equal to a which is 7 plus n minus 1 d is 7 by 2. Here there is one unknown that is n so we will find this. So here we get now 84 implies 84 is equal to 7 plus 7 n by 2 minus 7 by 2 which implies 7 n by 2 is equal to 84 minus 7 plus 7 by 2 which implies 7 n by 2 is equal to taking two others here so we get 168 minus 14 plus 7 which is implies 7 n by 2 is equal to 161 by 2. Now we see that this 2 gets cancels so which implies n is equal to 161 by 7. Now using this value of n we will find the sum which is equal to n by 2 multiplied by a plus a n. Now which is equal to n is equal to 161 by 7 divided by 2 so we multiply by 1 by 2 multiplied by a is 7 and a n is 84. So solving it further we get which is equal to 161 by 14 multiplied by 91. Now this gets cancels 7 twos are 14 and 7 thirteens are 91. So it is equal to 2093 by 2 which is equal to 10461 by 2 therefore required sum is 10461 by 2. I hope you understood the problem by and have a nice day.