Page 1: Introduction to Arithmetic Sequences
This page introduces the concept of arithmetic sequences and provides essential formulas and examples.
Definition: An arithmetic sequence is a series of numbers where each subsequent term differs from the previous one by a constant value, known as the common difference.
The page covers the following key points:
• Components of an arithmetic sequence: first term (a₁), common difference (r), and subsequent terms
• Examples of increasing and decreasing arithmetic sequences
• Ciąg arytmetyczny wzory (Arithmetic sequence formulas) for finding the nth term and the sum of n terms
Example: In the sequence 2, 4, 6, 8, the common difference (r) is 2, and it's an increasing sequence.
Highlight: The formula for the nth term of an arithmetic sequence is aₙ = a₁ + (n-1) • r, where a₁ is the first term, n is the position of the term, and r is the common difference.
The page also introduces the wzór na sumę ciągu arytmetycznego (formula for the sum of an arithmetic sequence): Sₙ = (n/2) • (a₁ + aₙ), where n is the number of terms, a₁ is the first term, and aₙ is the last term.
Vocabulary:
• Ciąg rosnący: Increasing sequence
• Ciąg malejący: Decreasing sequence
• Wyrazy ciągu: Terms of the sequence
