11 The first three terms of a geometric sequence are \(5 k - 2,3 k - 6 , k + 2\), where \(k\) is a constant.
- Show that \(k\) satisfies the equation \(k ^ { 2 } - 11 k + 10 = 0\).
- When \(k\) takes the smaller of the two possible values, find the sum of the first 20 terms of the sequence.
- When \(k\) takes the larger of the two possible values, find the sum to infinity of the sequence.