 Hi, I am Kanika and I am going to help you to solve the following question. The question says, find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, 1 by 2. Let's now begin with the solution. Let S denote the sum of product corresponding of the sequences 16, 32, 128, 32, 8, 2, 1 by 2. Now S is equal to 2 into 128 plus 4 into 32 plus 8 into 8 plus 16 into 2 plus 32 into 1 by 2. That is, S is equal to 256 plus 128 plus 64 plus 32 plus 16. We know that sum of n terms of Gp that is Sn is given by a into 1 minus r to the power n upon 1 minus r if r is less than 1. Now here, a that is first term is equal to 256, r that is common ratio is equal to 128 by 256 and this is equal to 1 by 2 and n is equal to 5 that is number of term. Now by substituting the value of a, r and n in this formula, we get S5 is equal to 256 into 1 minus 1 by 2 to the power 5 upon 1 minus 1 by 2. Now this is equal to 256 into 2 into 1 minus 1 by 32 and this is equal to 256 into 2 into 31 by 32. On dividing 256 by 32, we get 8. So this is equal to 16 into 31 and 16 into 31 is 496. Hence the required sum is 496. This is the required answer so this completes the session. Bye and take care.