The first three terms of a geometric progression are $3k$, $5k - 6$ and $6k - 4$, in that order.
(i)[2]
Show that $k$ satisfies the equation $7k^2 - 48k + 36 = 0$.
(ii)[4]
Find, showing all necessary working, the exact values of the common ratio for each possible value of $k$.
(iii)[2]
One of these ratios produces a convergent progression. Find the sum to infinity.
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