 Hello and welcome to the session. I am Arsha and I am going to help you with the following question which says if the sum of n terms of an APS pn plus q square where p and q are constants, find the common difference. So, let us now begin with the solution and we have given that sum of n terms it is denoted that Sn is equal to pn plus qn square APB A1 A2 A3 and so on. So, let us first find the first term which we get by replacing n by 1. So, A1 is equal to p into 1 plus q into 1 square which is equal to p plus q. So, this is the first term. Now, let us find the sum of 2 terms that will be A1 plus A2 sum is equal to S2. So, this will be equal to p into 2 plus q into 2 square. So, this is equal to 2p plus 4q. Now, we will find the second term of the AP that is A2 and it can be written as A2 plus A1 minus A1. So, A2 plus A1 is the sum of first 2 terms which is 2p plus 4q minus A1. So, A1 is the first term which is p plus q which on further simplifying comes equal to 2p plus 4q minus p minus q which is equal to p plus 3q. So, the second term of the AP is p plus 3q and the first term of the AP is p plus q and we know that common difference we get by subtracting A1 from A2 that is p plus 3q minus p plus q. So, this is equal to p plus 3q minus p minus q which is equal to 2q. Therefore, the common difference is equal to 2q. So, this completes the session. Take care and have a good day.