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MathNet 2019-part-06 — 184 problems (EN–VI) Question 142

Math Olympiad Vault · MathNet 2019-part-06 — 184 problems (EN–VI)

Question 142

The real solutions of the equation $x^{4}-x^{3}-2 x-4=0$ are the first two terms of a decreasing arithmetic sequence with 40 terms.
a) Compute the first two terms and the common difference of the sequence.
b) Compute the last term and write the general term $a_{n}$ of the sequence.
c) Compute the sum of all terms of the sequence with odd indices.