Final answer:
To find the sum of the 11th term of a geometric progression (G.P.), we need to first find the common ratio (r) of the G.P. By solving a quadratic equation, we can find the values of 'a' and 'r', and then use the sum of G.P. formula to find the sum of the 11th term.
Step-by-step explanation:
To find the sum of the 11th term of a geometric progression (G.P.), we first need to find the common ratio (r) of the G.P. From the given information, the sum of the 4th term and the 8th term is 15/2 and 255/32, respectively.
Let's denote the first term of the G.P. as 'a' and the common ratio as 'r'.
Using the formula for the sum of a G.P., we can write the following equations:
a * (1 - r^4) / (1 - r) + a * (1 - r^8) / (1 - r) = 15/2 + 255/32
48a * (1 - r^4) + 32a * (1 - r^8) = 480 + 255
3(1 - r^4) + 2(1 - r^8) = 15 + 8
3r^4 - 3 + 2r^8 - 2 = 23r^4 - 23
2r^8 - 3r^4 + 18 = 0
Solving this equation may require advanced mathematical techniques. Once you find the values of 'a' and 'r', you can use the formula for the sum of a G.P. to find the sum of the 11th term.