Algebra 1B Unit 1 Lesson 5 Flashcards

Sequences and Formulas

• The common difference in the sequence {17, 11, 5, -1, -7} is -6, indicating a consistent decrease between terms.
• A sequence starting with 9, where each term increases by 4, has a recursive formula: a1 = 9 and an = an-1 + 4.
• For the sequence a1 = 10, a2 = 6, a3 = 2, a4 = -2, the recursive formula is a1 = 10 and an = an-1 - 4, demonstrating a consistent decrease.
• The sequence {-4, -1, 2, 5, ...} has a recursive formula of f(1) = -4 and f(n+1) = f(n) + 3, indicating a consistent increase.

Explicit Formulas and Terms

• The explicit formula an = -1 + 3(n - 1) yields a 55th term of 161, calculated by substituting n = 55 in the formula.
• For the formula an = -2 + 32(n - 1), the 21st term is calculated as 28.
• The term derived from the formula an = 12 - 5(n - 1) for n = 30 is -133, indicating a decrease in value as n increases.

Graphs and Function Representation

• The explicit formula for the arithmetic sequence represented in the table (1, -2), (2, 3), (3, 8), (4, 13) is an = -2 + 5(n - 1), indicating a slope of 5.
• The graph implies an explicit formula f(n) = 1 - 3(n - 1) showcasing a linear decrease influenced by the coefficient of n.

Additional Functions and Transitions

• The arithmetic sequence {20, 23, 26, 29, 32} can be represented as f(n) = 3n + 17, reflecting a steady increase of 3 for each subsequent term.
• For a sequence starting at a1 = 22 with the recursive definition an = an-1 - 10, the equivalent explicit formula is an = 22 - 10(n - 1).
• An explicit formula an = -4 + 7(n - 1) corresponds to the recursive formula a1 = -4 and an = an-1 + 7, demonstrating an additive relationship among terms.