Grades 9-10 Video Solutions 2013-Level 9&10 Video Solutions 2013 problem24

Level 9&10 Video Solutions 2013 problem24

Video Transcription

Video Summary

Julio's procedure replaces each number in a set of three with the sum of the other two numbers. Beginning with the set {1, 2, 3}, he applies this repeatedly. Observing the pattern, the largest number in each sequence is twice the previous largest number minus one, generating a sequence: 3, 5, 9, 17, 33, etc. This grows rapidly, and by extrapolating, the pattern never exactly hits 2013 in the sequence. Therefore, Julio will never produce a set containing the number 2013, concluding that it is impossible, hence the answer is E.

Keywords

number sequence

pattern

set transformation

extrapolation

impossible outcome