 Hi, and welcome to the session. Let us discuss the following question. The question says that some of first three terms of a GP is 60. And the sum of the next three terms is 128. Determine the first term, the common ratio, and the sum to n terms of the GP. Let's now begin with the solution. Let a be the first term, the common ratio of the GP. Determine the first term, and r is the common ratio. Therefore, GP is of the form a, a r, a r squared, a r cubed, a r 4, a r 5, and so on. Now in the question, it is given that sum of first three terms of a GP is 60. So this means a plus a r, plus a r squared is equal to 60. Let's name this equation as equation number one. And it is also given in the question that sum of the next three terms is 128. That means a r cubed, a r 4, r 5 is equal to 128. Let's name this equation as equation number two. Now on dividing, we get a r cubed plus a r 4 plus a r 5 upon a plus a r, plus a r squared is equal to 128 by 60. Now this implies a r cubed into 1 plus r plus r squared upon a into 1 plus r plus r squared is equal to, on dividing 128 by 16, we get 8. And this implies r cubed is equal to a. Since one can say a into 1 plus r plus r squared from both numerator and denominator, we are left with only r cubed. And this implies r is equal to 2. We'll find the value of a. So let's now substitute value of r in 1. By substituting the value of r in 1, we get a plus a into 2 plus a into 4 is equal to 60. And this implies 7a is equal to 16. And this implies a is equal to 16 by 7. So the first term of the GP is 16 by 7. Now we will find sum to n terms of this GP. We know that when r is greater than 1, then sum to n terms of GP, that is, sn is equal to a into r to the power n minus 1 upon r minus 1 if r is greater than 1. Right. Now here, a is equal to 16 by 7 and r is equal to 2. So sum to n terms of this GP, that is, sn is equal to 16 by 7 into 2 to the power n minus 1 upon 2 minus 1. And this is equal to 16 by 7 into 2 to the power n minus 1. Hence, the required first term is 16 by 7. Common ratio is 2. And sum to n terms of this GP is 16 by 7 into 2 to the power n minus 1. This is the required answer. So this completes the session. Bye and take care.