## Exam-Style Question on Sequences## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 470. This question is similar to one that appeared on an A-Level paper (specimen) for 2017. The use of a calculator is allowed.

In a geometric series the common ratio is \(r\) and sum to \(n\) terms is \(S_n\).

Given that \(S_4 = \frac{8}{9} S_{\infty} \) and \(r = \pm \frac{1}{\sqrt{k}} \) find the value of \(k\).

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