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.

Page 1: Fundamentals of Arithmetic and Geometric Sequences

This page introduces the core concepts of arithmetic and geometric sequences, providing essential formulas and examples.

Definition: An arithmetic sequence has a constant difference (reason) between consecutive terms, while a geometric sequence has a constant ratio.

Example: Arithmetic sequence with reason +4: {0, 4, 8, 12} Example: Geometric sequence with ratio x2: {2, 4, 8, 16}

The page demonstrates how to prove a sequence is arithmetic using the formula Un+1 = Un + R, where R is the common difference. It also explains the variation of arithmetic sequences:

Highlight: For arithmetic sequences:

• If R > 0: Increasing sequence
• If R < 0: Decreasing sequence
• If R = 0: Constant sequence

The graphical representation of arithmetic sequences is discussed, emphasizing that points are plotted but not connected, forming a cloud of points.

Vocabulary: Linear growth - describes the pattern of an arithmetic sequence when graphed