Algebra I Regents Review - Sequences
Regents Review Lesson #8: Sequences
Homework: See board/website
Warm Up
(Modeled from #4 on the August 2015 Regents)
The graph of f(x) is shown below.
y
Which function would have the same
roots as f(x)?
1) g(x) = (x + 2)(x2 – 5x – 4)
2) h(x) = (x – 2)(x2 + 5x + 4)
x
3) j(x) = (x – 2)(x2 – 5x – 4)
4) k(x) = (x + 2)(x2 + 5x + 4)
Review of Arithmetic Sequences
A pattern where a common difference, d, exists between each term.
Examples:
2, 5, 8, 11, 14, ... (adding by 3 each term)
1, -4, -9, -14, ... (adding by -5 each term)
Formulas to Know
Recursive:
An = An – 1 + d, A1 = __ for n ≥ 2
Explicit:
An = A1 + (n – 1)d
*(this formula is provided for the Regents)
Algebra I Regents Review - Sequences
Review of Geometric Sequences
A pattern where a common ratio, r, exists between each term.
Examples:
3, 12, 48, ... (multiplying by 4 each term)
-8, 4, -2, 1, ... (multiplying by -1/2 each term)
Formulas to Know
Recursive:
An = An – 1 • r, A1 = __ for n ≥ 2
Explicit:
A n = A 1 rn – 1
*(this formula is provided for the Regents)
Other Types of Recursive Sequences
Not all sequences are arithmetic or geometric. Some follow a different pattern
and we may need to use the recursive rule to figure out the terms.
Ex: Given f(n) = -2f(n – 1) + 3 and f(1) = -5, find f(3).
Algebra I Regents Review - Sequences
Skill Practice
1. The third term in an arithmetic sequence is 2 and the fifth term is -1.
Part A: Write an explicit formula for this sequence.
Part B: Use your formula to find the 10th term of this sequence.
2. If a sequence is defined recursively by f(0) = 3 and f(n + 1) = 2f(n) – 1 for n ≥ 0,
find f(2).
Sample Regents Question
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Algebra I Regents Review - Sequences
Sample Regents Question
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Sample Regents Question
3)
Algebra I Regents Review - Sequences
Sample Regents Question
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Sample Regents Question
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Algebra I Regents Review - Sequences
Sample Regents Question
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Sample Regents Question
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Algebra I Regents Review - Sequences
Sample Regents Question
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Summary
In your Regents notebook, write down the 3 most important things to remember
from this lesson
- These can be strategies, tips, things to watch out for, etc..
Exit Slip