Page 1: Solving Sequence Problems

This page presents a detailed examination of ciągi zadania maturalne PDF, focusing on solving equations to determine if given numbers are terms in specific sequences.

The problem involves a sequence with the general term an = 4n + 2 / 16 - n. Students are tasked with identifying which of the given numbers (30, 9, 5, 46) are terms in this sequence.

Definition: A sequence term is a number that satisfies the general formula of the sequence for some integer value of n.

The solution process involves:

1. Setting up equations using the general term formula and the given numbers.
2. Solving these equations to find the value of n.
3. Checking if the resulting n is a positive integer.

Example: For 30, the equation is 30$16-n$ = 4n+2, which simplifies to -66n = -726. Solving this gives n = 11, confirming 30 is a term in the sequence.

Highlight: It's crucial to verify that the calculated n is a positive integer. If n is not an integer or is negative, the number is not a term in the sequence.

The page also shows detailed calculations for other numbers:

• For 9: 9$16-n$ = 4n+2, leading to n = 15
• For 46: 46$16-n$ = 4n+2, resulting in n ≈ 11.03 (not an integer, thus not a term)
• For 30: Calculation confirms it's a term $n = 7$

Vocabulary: "Wyraz ciągu" means "term of the sequence" in Polish.

This comprehensive approach to ciągi zadania z rozwiązaniami provides students with a clear methodology for tackling similar problems in their ciągi zadania maturalne rozszerzony exams.