 Hello and welcome to the session. In this session we will discuss a question which says that in an AP, which is Arthematic Progression, the first term is 2, the last term is 29 and some of the terms is 155. Find the common difference of the AP. Now before starting the solution of this question, we should know some results. And that is, sum of n terms of an AP when first term and last term is given by, that means the sum of n terms is equal to n by 2 into A plus L the whole, where is the first term, is the last term, are the number of terms also, the last term in AP, that is L is equal to A plus L minus 1 the whole into D, where D is the common difference. Now these results will work out as a key idea for solving out this question. And now we will start with the solution. Here the first term is given as 2, the last term is 29 and some of the terms is 155. So here it is given the first term of an AP, A is equal to 2, the last term of an AP, L is equal to 29, the sum of the terms of an AP, SN is equal to 155. And we will have to find the common difference D of an AP. Now by using the formula which is given in the key idea, n terms, that is SN is equal to n by 2 into A plus L the whole. Now putting the values of SN, L and A here, this implies 155 is equal to n by 2 into 2 plus 29 the whole. This implies 155 into 2 is equal to n into 31. This implies 155 into 2 over 31 is equal to n. Now this implies here, 31 into 5 is 155 and 5 into 2 is 10, so 10 is equal to n. All you can say n is equal to 10. Therefore the number of terms in an AP is equal to 10. Now using this formula which is given as a key idea, we have last term that is L is equal to A plus L minus 1 the whole into D. Now putting the values of L, A and L here, this implies 29 is equal to 2 plus 10 minus 1 the whole into D. Further this implies 29 minus 2 is equal to 19. This implies 27 by 9 is equal to D. This implies here 9 into 3 is 27, so D is equal to 3. Therefore common difference of an AP that is D is equal to 3. So this is the solution of the given question and that's all for the session. Hope you all have enjoyed the session.