 Hello and welcome to the session. Let us understand the following problem today. In an AP given A3 is equal to 15, F10 is equal to 125, find D and A10. Now let us write the solution. We have A3 is equal to A plus N minus 1D, where N is equal to 3. So A3 is equal to A plus 2D. Now given to us A3 is equal to 15 which is equal to A plus 2D. Now here D is equal to 15 minus A by 2. Now it is given to us that S10 is equal to 125. So we know the formula that SN is equal to N by 2 multiplied by 2A plus N minus 1D. SN that is S10 given to us as 125 which is equal to N is 10 by 2 multiplied by 2A plus 10 minus 1D. We substitute it from here that is 15 minus A by 2. Now here we can see that there is only one unknown that is A. Now solving this equation for A it implies 125 is equal to, this gets cancelled by 5. So 5 multiplied by 2A plus 9 multiplied by 15 minus A by 2 which implies 125 is equal to 10A plus 45 multiplied by 15 minus A by 2 which implies 125 is equal to 10A which is equal to, sorry, plus 45 into 15 by 2 minus 45A by 2. Now taking all the right terms of A on left hand side we get which implies 45A by 2 minus 10A is equal to 45 into 15 by 2 minus 125. Now which implies taking LCM as 2 here we get 45A minus 20A which is equal to, again taking LCM as 2 here we get 45 into 15 minus 250. Now we can see that this 2 and this 2 gets cancelled so we get 45 minus 20A which is equal to 25A which is equal to taking 25 common we get 27 minus 10. Now we can see that this 25 gets cancelled with this A so we are left with A is equal to 27 minus 10 which implies A is equal to 17. Now using this value of A we find D as we have earlier found that D is equal to 15 minus A by 2 so which is equal to 15 minus 17 by 2 which is equal to minus 2 by 2 which is equal to minus 1 therefore D is equal to minus 1. Now we have to find A10. A10 is equal to A plus N minus 1B. N is equal to 10 so it is equal to A plus 9D. Now A is equal to 17 plus 9 multiplied by D is equal to minus 1 so it is equal to 17 minus 9 which is equal to 8 therefore D is equal to minus 1 and A10 is equal to 8 which is our required answer. I hope you understood the question. Bye and have a nice day.