Mathegoras

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Common ratio from a sum relation

High school · ●●●○○ 50 pts

Let SnS_n be the sum of the first nn terms of a geometric sequence {an}\{a_n\} with nonzero first term and common ratio qq. Given that S4=5S2S_4 = 5S_2, find all possible values of qq, listed in increasing order.

Enter the values in any order.

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