- The first three terms of a geometric sequence are
$$3 k + 4 \quad 12 - 3 k \quad k + 16$$
where \(k\) is a constant.
- Show that \(k\) satisfies the equation
$$3 k ^ { 2 } - 62 k + 40 = 0$$
Given that the sequence converges,
- find the value of \(k\), giving a reason for your answer,
- find the value of \(S _ { \infty }\)