 Hi and welcome to the session. I am Shashi and I am going to help you to solve the following question. Question is fill in the blanks in the following table. Given that A is the first term, D is the common difference and An is the nth term of the AP. Given table is this. First of all let us understand the key idea to solve the given question. The nth term An of the AP with first term A and common difference D is given by An is equal to A plus n minus 1 multiplied by N. Let us start with the solution now. First of all we can see in first part we have given A, D and N and we have to find out the nth term. So we know by key idea nth term is given by the formula A plus n minus 1 multiplied by D where A is the first term and D is the common difference. Now this implies An is equal to 7 plus 8 minus 1 multiplied by 3. Here we have substituted the value of An and D from this table. Now we get nth term is equal to 7 plus 7 multiplied by 3 or we can say An is equal to 28. Now this completes the first part of the question. Now in the second part we have to find the value of D that is the common difference and we are given An and the value of N. Now again we know nth term is equal to A plus n minus 1 multiplied by D as we have already read in key idea. Now we have to find the D and we will substitute the values of An, An and N given in the second part to find D. Now we can write 0 is equal to minus 18 plus 10 minus 1 multiplied by D. Now this implies 0 is equal to minus 18 plus 90 or we can say this implies 90 is equal to 18. This further implies D is equal to 18 upon 9 equal to 2. So we get D is equal to 2. Now in the third part we have to find the value of A and we are given the value of common difference that is D, N and An. Now we will use the formula for nth term that is An is equal to A plus N minus 1 multiplied by D. So we know nth term is equal to minus 5, A plus value of N is equal to 18 and value of D is equal to minus 3. So we have substituted for An, N and D. Now this implies minus 5 is equal to A minus 51 and this further implies A is equal to minus 5 plus 51. This implies A is equal to 46. Therefore we get A is equal to 46. Now in the fourth part we are given A, D and An and we have to find the value of N. Now again we will use the formula for nth term and substitute for A, D and N and find the value of N. So we can write An is equal to A plus N minus 1 multiplied by D. Now we know An is equal to 3.6, A is equal to minus 18.9. We have to find N and value of D is 2.5. So we have substituted for An, A and D. Now this implies 3.6 plus 18.9 is equal to 2.5 multiplied by N minus 1. Now this implies 22.5 is equal to 2.5 multiplied by N minus 1. This further implies N minus 1 is equal to 22.5 upon 2.5. Now this implies N minus 1 is equal to 9. This implies N is equal to 9 plus 1 equal to 10. Therefore we get the value of N is equal to 10. Now in the fifth part we are given A, D and N and we have to find the value of N. So again we will use the formula for nth term that is A plus N minus 1 multiplied by D. So we can write An is equal to A plus N minus 1 multiplied by D. Now we have to find N and we will substitute the values of An and D. Now we know An is equal to 3.5 plus 105 minus 1 multiplied by 0. Now this implies An is equal to 3.5 plus 0. This further implies An is equal to 3.5. So we get An is equal to 3.5. So our final answer is for first part An is equal to 28 for second part. Common difference is equal to 2 for third part. A is equal to 46 that is the first term. Then for fourth part N is equal to 10 for fifth part An is equal to 3.5. So this is our required answer. This completes the session. Hope you understood the session. Take care and goodbye.