 Hi, and welcome to our session. Let us discuss the following question. The question says, show that the product of the corresponding terms of the sequence is A ar ar square ar to the power n minus 1, and A ar ar square ar to the power n minus 1. Form OGP and find the common ratio. Let's now begin with the solution. Given two sequences are A ar ar square so on up to A ar to the power n minus 1, and A ar ar square so on up to A ar to the power n minus 1. We have to show that product of the corresponding terms of these two sequences form OGP. So let's now find the product of corresponding terms of these two sequences. Now product of corresponding terms given two sequences is equal to A into A ar into A ar ar square into A ar square so on A ar to the power n minus 1 into A ar to the power a minus 1. Now this sequence can be written as A A A into A ar A A into R square R square so on into R to the power n minus 1 into R to the power n minus 1. Now this can further be written as A A A A A A into R ar square so on A A into R to the power n minus 1. Now clearly this is a GP. It's first term A A common ratio since on divided the second term that is A A into R first term that is A A we get R R. And this ratio remains the same throughout this sequence. Hence the required common ratio is R A. This is our required answer. So this completes the session. Bye and take care.