Page 2: Advanced Concepts and Variations in Sequences
This page delves deeper into the properties of arithmetic and geometric sequences, focusing on their graphical representations and variations.
Highlight: For geometric sequences:
- If q > 1: Increasing sequence
- If 0 < q < 1: Decreasing sequence
- If q = 1: Constant sequence
The page provides techniques for proving a sequence is geometric using the formula Un+1 = Un × q, where q is the common ratio.
Example: Geometric sequence {2, 6, 18, 54, 162} with ratio q = 3
It's emphasized that while aligned points in a graph may suggest an arithmetic sequence, this observation alone is not sufficient to prove it definitively.
Vocabulary: Conjecture - to form an opinion or supposition based on incomplete information
The page concludes with a note on the importance of verifying the consistency of the ratio or difference throughout the sequence before classifying it as geometric or arithmetic.
Highlight: A sequence is not necessarily geometric if the ratio between two consecutive terms is not constant throughout the entire sequence.
This comprehensive guide serves as an excellent fiche révision suite arithmétique et géométrique PDF for students preparing for controle suites STMG or working on exercices corrigés suites Terminale STMG pdf.
