9. The first three terms of a geometric sequence are
$$7 k - 5,5 k - 7,2 k + 10$$
where \(k\) is a constant.
- Show that \(11 k ^ { 2 } - 130 k + 99 = 0\)
Given that \(k\) is not an integer,
- show that \(k = \frac { 9 } { 11 }\)
For this value of \(k\),
- evaluate the fourth term of the sequence, giving your answer as an exact fraction,
- evaluate the sum of the first ten terms of the sequence.