7. (i) A geometric sequence has first term 4 and common ratio 6
Given that the \(n ^ { \text {th } }\) term is greater than \(10 ^ { 100 }\), find the minimum possible value of \(n\).
(ii) A different geometric sequence has first term \(a\) and common ratio \(r\).
Given that
- the second term of the sequence is - 6
- the sum to infinity of the series is 25
- show that
$$25 r ^ { 2 } - 25 r - 6 = 0$$
Write down the solutions of
$$25 r ^ { 2 } - 25 r - 6 = 0$$
Hence,state the value of \(r\), giving a reason for your answer,find the sum of the first 4 terms of the series.
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