The first term of a geometric progression is 50 and the common ratio is 0.8 . Use logarithms to find the smallest value of \(k\) such that the value of the \(k\) th term is less than 0.15 .
In a different geometric progression, the second term is - 3 and the sum to infinity is 4 . Show that there is only one possible value of the common ratio and hence find the first term.
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