 Hi and welcome to this session. Let us discuss the following question. The question says find a GP for which the sum of the first two terms is minus 4 and the fifth term is 4 times the third term. Let's now begin with the solution. Let A be the first term and R be the common ratio of the given GP. Now in the question it is given that sum of the first two terms is minus 4. That means T1 plus T2 is equal to minus 4 and it is also given in the question that fifth term is 4 times the third term. That means T5 is equal to 4 times the third term that is T3. Since A is the first term and R is the common ratio therefore terms of GP are of the form A, AR, AR2, AR4 and so on. T2 is equal to minus 4 therefore it clearly implies that A plus AR is equal to minus 4 and T5 is equal to 4 into T3 implies AR4 is equal to 4 AR2. Now this implies AR4 upon AR2 is equal to 4 and this implies AR2 is equal to 4 and this implies AR is equal to plus minus 2. Now we will find the value of A. Let's name this equation as equation number 1. When R is equal to 2 then equation 1 reduces to A plus A into 2 is equal to minus 4 and this implies 3 is equal to minus 4 and this implies A is equal to minus 4 by 3. Now when R is equal to minus 2 then equation 1 reduces to A plus A into minus 2 is equal to minus 4. This implies minus A is equal to minus 4 and this implies A is equal to 4. When R is equal to 2 and A is equal to minus 4 by 3 then the GP is minus 4 by 3 minus 8 by 3 minus 16 by 3 and so on. And when R is equal to minus 2 and A is equal to 4 then the GP is 4 minus 8, 60 minus 32, 64 and so on. Hence the required GP is minus 4 by 3 minus 8 by 3 minus 16 by 3 and so on or 4 minus 8, 60 minus 32, 64 and so on. This is our required answer. So this completes the session. Bye and take care.