 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says the sum of some lump terms of GP is 315 whose first term and the common ratio of 5 and 2 respectively find the last term and the number of terms. Let us now begin with the solution and let the number of terms of GP is equal to n. So, we are given that sum of n terms is equal to 315 and also we are given that the first term let us denote it by small a is equal to 5 the common ratio small r is equal to 2 which is greater than 1. The sum of a GP series is a into r raise to the power n minus 1 upon r minus 1. So, on substituting the values we have 315 is equal to 5 to 2 raise to the power n minus 1 on 2 minus 1 on 15 cone 5 is equal to 2 raise to the power n minus 1 or we have 63 is equal to 2 raise to the power n minus 1. So, 2 raise to the power n is equal to 64 which can be written as 2 raise to the power 6. So, on comparing we find that n is equal to 6. Now, let us find the last term a GP series is of the fact a here are 3 and so on where a is the first term and r is the common ratio. Now, here we have a is equal to 5 and r is the common ratio which is given to us as 2 to find the last term and that will be the sixth term. The sixth term is given by a raise to the power 5 and this is the first term. Second term is given by a into r raise to the power 1. Third term is given by a into r raise to the power 2. So, the sixth term is given by a into r raise to the power 5. So, a is 5, r is 2, 2 raise to the power 5 so we have 5 into 32 which is equal to 160. Therefore, our answer is the last term is equal to 160 the value of n is 6. So, this completes the solution. Take care and have a good day.