- The first 3 terms of a geometric sequence are
$$3 ^ { 4 k - 5 } \quad 9 ^ { 7 - 2 k } \quad 3 ^ { 2 ( k - 1 ) }$$
where \(k\) is a constant.
- Using algebra and making your reasoning clear, prove that \(k = \frac { 5 } { 2 }\)
- Hence find the sum to infinity of the geometric sequence.