Page 1: Understanding Arithmetic Sequences

This page introduces the fundamental concepts of arithmetic sequences and their properties, focusing on identification and calculation methods.

Definition: An arithmetic sequence is a sequence where the difference between successive terms remains constant.

Vocabulary: Common difference (d) - The constant difference between consecutive terms in an arithmetic sequence.

Example: In the sequence 1, 5, 9, 13, ..., the common difference is 4.

Highlight: The nth term formula for arithmetic sequences is an = a₁ + (n-1)d, where:

• a₁ is the first term
• n is the position of the term
• d is the common difference

Example: For a sequence with a₁ = 3 and d = 2:

• The formula becomes an = 3 + 2(n-1)
• Simplified to an = 2n + 1