 Hello and welcome to the session. In this session we will discuss a question which says that in an AP that is Arithmetic Preversion, the sum of first-hand terms is minus 150 and the sum of its next-hand terms is minus 550. Find the AP. Now before starting the solution of this question, we should know some results. And first is the sum of first-hand terms of an AP is Sn is equal to n by 2 into, to have this n minus 1, the whole, into D, the whole. Where A is the first term of the AP and D is the common difference. And secondly, any AP can be written as A, A plus D, A plus 2D, A plus 3D and so on. Where A is the first term and D is the common difference of the AP. Now these results will work out as a key idea for solving out this question. And now we will start with the solution. Now it is given in the question that the sum of first-hand terms of an AP is minus 150 and the sum of its next-hand terms is minus 550. So given the sum of 10 terms in an AP that is S10 is equal to minus 150. Now 20 terms is equal to S20. The second written as S10 terms in an AP plus sum of next 10 terms in an AP. Now sum of first-hand terms is minus 150 and sum of next-hand terms is minus 550. So putting these values here, this implies S20 is equal to minus 150 plus or minus 550 which is equal to minus 150 minus 550 which is equal to minus 700. Now using this result which is given in the key idea, for m is equal to 10 is equal to 10 out of 2 into 2A minus 1 that is 10 minus 1 the whole into D the whole. Now putting the value of S10, this implies minus 150 is equal to 5 into 2A plus 90 the whole. Which further implies minus 150 by 5 is equal to 2A plus 90 which implies minus 30 is equal to 2A plus 90 and we can write 2A plus 90 is equal to minus 30 and that is named as equation as 1. For m is equal to 20, the sum of first 20 terms that is S20 is equal to 20 by 2 into 2A plus n minus 1 that is 20 minus 1 the whole into D the whole. Now we have S20 as minus 700. Now putting this value here, this implies minus 700 is equal to 10 into 2A plus 19 D the whole which implies minus 700 by 10 is equal to 2A plus 19 D which further implies 2A plus 19 D is equal to minus 70. And that is named as equation number 2. Now this is the equation number 1 and this is the equation number 2. Now subtracting 1 from 2 we get 2A plus 19 D minus 2A plus 9 D the whole is equal to minus 70 minus of minus 30. Now what implies 2A plus 19 D minus 2A minus 9 D is equal to minus 70 plus 30 which further implies now these terms will be cancelled with each other so it will be 10 D is equal to minus 40 which further implies D is equal to minus 40 by 10 which is equal to minus 4. Now this is the equation number 1. Now putting D is equal to minus 4 in 1 we get plus 9 into minus 4 is equal to minus 30 which implies minus 36 is equal to minus 30 which further implies equal to minus 30 plus 30 which implies 2A is equal to 6. Which further gives A is equal to 3. Now using this result which is given in the key idea for A is equal to 3 D is equal to minus 4 the required AP is 3 3 plus of minus 4 3 plus 2 into minus 4. That is 3 3 minus 4 minus 12 and so on. And that is 3 3 minus 4 is minus 1 3 minus 8 is minus 5 3 minus 12 is minus 9 and so on. So this is the required AP and this is the solution of this question. That's all for this session. Hope you all have enjoyed the session.