lean_workbook_plus_4945

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Let $a_i$ be the geometric sequence and $b_i$ be the arithmetic sequence. Then we have: \n $a_1+b_1=7$ \n $a_1r +b_1 +r=26$ and \n $a_1 r^2 +b_1+2r= 90$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_4945 (a b r : ℝ) (h₁ : a + b = 7) (h₂ : a * r + b + r = 26) (h₃ : a * r^2 + b + 2 * r = 90) : a = 2 ∧ b = 5 ∧ r = 3   :=  by sorry

The second real solution and any sequence restrictions require a complete classification, which this audit does not supply.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Remove the invented triple(2,5,3) and solve the stated system, including(5,2,4).

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.