 Hello and welcome to the session, let us understand the foreign question which says, in an AP given D is equal to 5, S9 is equal to 75, find A and A9. Now let's proceed on to the solution. Given to us is D as 5 and S9 as 75 and we have to find A and A9. We know Sn is equal to N by 2 multiplied by 2A plus N minus 1D, where N is the number of terms, A is the first term and D is the common difference. Sn that is S9 is given to us as 75, so it can be written as 75 is equal to N is equal to 9, 9 by 2 divided by 2 multiplied by A plus 9 minus 1D is given as 5, so multiplied by 5. It implies taking 2 on right hand side, so we get 150 is equal to 9 multiplied by 2A plus 9 minus 1 is 8, 8 multiplied by 5 which implies 150 is equal to 9 multiplied by 2A plus 40. This implies 150 is equal to 9 multiplied by 2A is 18A plus 9 multiplied by 40 is 360. This implies 18A is equal to 150 minus 360. This implies 18A is equal to minus 210 that is A is equal to minus 210 by 18. Now it cuts by 9 and 210 gets cancelled by 2 and we get here 70. Now 9 gets cancelled by 3 and we get here 3 and similarly 70 gets cancelled by 3 and we get here 35 which is equal to minus 35 by 3. Therefore A is equal to minus 35 by 3. Now we have to find A9. A9 is equal to A plus 8D which is equal to A is equal to minus 35 by 3 plus 8 multiplied by D. D is equal to 5 which is equal to minus 35 by 3 plus 40. Now taking LCM we get 3 so we get here minus 35 plus 120 which is equal to minus 85 by 3. Therefore A9 is equal to minus 85 by 3. Hence A is equal to minus 35 by 3 and A9 is equal to minus 85 by 3 and this is our required answer. I hope this is clear to you. Bye and have a nice day.