IL-GILLIS 2018 Problem 2

An arithmetic sequence is an infinite sequence of the form $a_n=a_0+n\cdot d$ with $d\neq 0$ .

A geometric sequence is an infinite sequence of the form $b_n=b_0 \cdot q^n$ where $q\neq 1,0,-1$ .

[list=a] [] Does every arithmetic sequence of integers have an infinite subsequence which is geometric? [] Does every arithmetic sequence of real numbers have an infinite subsequence which is geometric? [/list]