 Hi and welcome to the session. Let us discuss the following question. The question says the sum of first three terms of a GP is 39 by 10 and their product is 1. Find the common ratio and the terms. Let's now begin with the solution. Let be the first terms of the GP. In the question it is given that sum of these terms is 39 by 10. So a by r plus a plus a r is equal to 39 by 10. Right. Now it is also given in the question that their product is 1. So this means a by r into a into a r is equal to 1. Now this implies a cube is equal to 1 and this implies a is equal to 1. By substituting a as 1 in this equation we get 1 by r plus 1 plus r is equal to 39 by 10. Now this implies 1 plus r plus r square by r is equal to 39 by 10 and this implies 10 plus 10 r plus 10 r square is equal to 39 r and this implies 10 r square minus 29 r plus 10 is equal to 0 and this implies 10 r square minus 25 r minus 4 r plus 10 is equal to 0 and this implies 5 r into 2 r minus 5 minus 2 into 2 r minus 5 is equal to 0 0 and this implies 5 r minus 2 into 2 r minus 5 is equal to 0 and this implies r is equal to 2 by 5 or r is equal to 5 by 2. r is equal to 2 by 5 then the terms of GPR by 2, 1 and 2 by 5 and when equal to 5 by 2 then the terms of GPR are required common ratio that is r is equal to 5 by 2 or 2 by 5 r is equal to 5 by 2 then the terms r this is our required answer so this completes the session bye and take care