 Hi and welcome to our session. Let us discuss the following question. The question says, given a GP with A is equal to 729 and 7 term 64 to term an S7. Let's now begin with the solution. In this question we have to find the sum of 7 terms. In the question we are given that the first term that is A is equal to 729 and 7 term that is D7 is equal to 64. For calculating this sum we need to know the first term common ratio and the number of terms. We know the first term and the number of terms so we have to only find the common ratio. Let R be the common ratio Now D7 is equal to 64. This implies A into R to the power 6 is equal to 64. A is equal to 729 it is given to us. So this implies 729 into R to the power 6 is equal to 64 and this implies R to the power 6 is equal to 64 by 729 and this implies R to the power 6 is equal to 2 by 3 to the power 6 and this implies R is equal to 2 by 3. Now 2 by 3 is less than 1 and we know that when R is less than 1 then sum of n terms is given by A into 1 minus R to the power n upon 1 minus R. So we can now easily find the sum of 7 terms. Now in given GP A is equal to 729 R is equal to 2 by 3 and since we have to find the sum of 7 terms therefore n is equal to 7. By substituting the values of A, R and n we get S7 is equal to 729 into 1 minus 2 by 3 to the power 7 upon 1 minus 2 by 3. Now this is equal to 729 into 3 to the power 7 minus 2 to the power 7 upon 3 to the power 7 upon 1 by 3 and this is equal to 729 into 3 to the power 7 minus 2 to the power 7 upon 3 to the power 7 into 3. Now 729 into 3 is 2187 so we have 2187 into 3 to the power 7 minus 2 to the power 7 upon 3 to the power 7 is equal to 7 sorry 2187. So this is equal to 3 to the power 7 minus 2 to the power 7 3 to the power 7 is equal to 2187 and 2 to the power 7 is equal to 128. Once we are finding 128 from 2187 we get 2059. Hence the required sum of 7 terms is 2059. This is our required answer so this completes the session. Bye and take care.