 Hi, and welcome to the session. Let us discuss the following question. The question says if A, B, C and D are in GP, show that A squared plus B squared plus C squared into B squared plus C squared plus D squared is equal to AB plus BC plus CD squared. Let's now begin with the solution. Let R be the common ratio of the GP, B, C and D. This is the common ratio. Therefore, the second term of this GP, that is B, is equal to ARC, that is third term is equal to AR squared and fourth term that is D is equal to ARQ. Now we will show that A squared plus B squared plus C squared into B squared plus C squared plus D squared is equal to AB plus BC plus CD squared. So let's now consider the left-hand side. Left-hand side is equal to A squared plus B squared plus C squared into B squared plus C squared plus D squared. Now substitute the value of B, C and D in this expression. By substituting the values, we get A squared plus A squared R squared plus A squared R to the power 4 into A squared R squared plus A squared R to the power 4 plus A squared R to the power 6. Now by taking A squared common from this expression, we get A squared into 1 plus R squared plus R to the power 4 and by taking A squared R squared common from this expression, we get A squared R squared into 1 plus R squared plus R to the power 4. Now this is equal to A to the power 4 R squared into 1 plus R squared plus R to the power 4 whole squared. Now consider the right-hand side. Right-hand side is equal to AB plus BC plus CD whole squared. Now substitute the value of B, C and D. So by substituting the values, we get A into AR plus AR into AR squared plus AR squared into AR cubed whole squared. Now this is equal to A squared R plus A squared R cubed plus A squared R to the power 5 whole squared. Now by taking A squared R common from this expression, we get A squared R into 1 plus R squared plus R to the power 4 whole squared and this is equal to A to the power 4 R squared into 1 plus R squared plus R to the power 4 whole squared. Our left-hand side is also equal to A to the power 4 R squared into 1 plus R squared plus R to the power 4 whole squared. Hence we have proved that right-hand side is equal to left-hand side. So this completes the session. Bye and take care.