Closed Interval Differences

★ 7/10Geometric Progression Set Theory algebra sequences Casework

Problem

A geometric sequence $\{a_n\}$ has first term $a_1 > 0$ and common ratio $q > 1$ . Define

l_n = \left\{x - y \mid x, y \in [a_1, a_2] \cup [a_n, a_{n+1}]\right\}.

If $l_n$ is a closed interval for every positive integer $n$ , find the range of possible values of $q$ .

Answer

Solution

Difficulty	7/10
Topics	Geometric Progression, Set Theory, algebra, sequences, Casework

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