8. (b) Three numbers whose sum is 27 are in arithmetical progression. If 1 is added to the first, 3 to the second, and 11 to the third, the sums will be in geometrical progression. Find the numbers.

8. (c) Derive the formula for the sum of n terms of a geometrical progression.

9. (a) Expand and simplify

9. (b) For what value of x will the ratio

be equal to the ratio

?