Avoiding Progressions

★ 7/10combinatorics Arithmetic Progression Counting Casework

Problem

The sequence $2, 3, 4, a, b, 20, 30, 40$ consists of positive integers and is strictly increasing. Suppose every strictly increasing sequence formed by choosing $4$ of its terms is neither arithmetic nor geometric. Find the number of ordered pairs $(a, b)$ .

Answer

Solution

Difficulty	7/10
Topics	combinatorics, Arithmetic Progression, Counting, Casework

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