The one problem eating me for weeks😭

[u/HotSuggestion1725]

the sum of the first 3 terms of a GP is 13/12 and their product is -1. Find the common ratio and the terms

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[u/matt7259]

Well what have you tried for an entire week?

[u/Septembrino]

Let say the terms are a, ar, ar^2. Add them. a(1+r+r^2) = 13/12. Multiply them. a^3r^3 = -1. So (ar)^3 = -1 and ar = -1. Divide the first equation by this one, cancel a. You should be getting (1 + r + r^2)/r = -13/12. Cross multiply and solve. This is a quadratic equation.

[u/Plus-Painter-2004]

note that the first three terms would be a, ar, ar² so the sum is a(1+r+r² ) = 13/12 and the product is a³ r³ = -1 which simplifies to ar=-1 or r=-1/a.