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Chapter 11 Sequences and Series
Algebra 2 Chapter 11 Sequences and Series
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11-2 Arithmetic Sequences
WARMUP: Simplify: -7 + (6 – 1)3 4 + (n – 1)(-2) Evaluate if n = 50: -3 + 4n 100 – (0.5)n Solve the system: 6 = x + y 14 = x + 5y
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11-2 Arithmetic Sequences
Objective: To find a formula for the nth term of an arithmetic sequence and to find specified terms of arithmetic sequences.
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11-2 Arithmetic Sequences
Say we have this arithmetic sequence: 3, 7, 11, 15, … We have a common difference of d = 4 So the next few terms would be… …, 15, 19, 23, … What if we wanted to know the 105th term of the sequence?
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11-2 Arithmetic Sequences
Quick note about notation. We designate the terms of the sequence from the previous example as follows: t1 t2 t3 t4 t5 … 3, 7, 11, 15, 19, … Therefore the 5th term is 19. The 3rd term is 11.
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11-2 Arithmetic Sequences
Look at initial example in book, p. 507. (99 differences)
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11-2 Arithmetic Sequences
IMPORTANT! In an arithmetic sequence with first term t1 and common difference d, the nth term (or general term) is given by
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11-2 Arithmetic Sequences
Examples: Let’s go back to the sequence we started with: 3, 7, 11, 15, … Find tn . Find t17 Find t3
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11-2 Arithmetic Sequences
Notice that the equation for the nth term works for ANY term in the sequence. To check, see if t1 matches the first number in your sequence…
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11-2 Arithmetic Sequences
More examples: Find a formula for the nth term of each sequence: -1, 0, 1, 2, … 30, 20, 10, 0, … -3, -10, -17, -24, … -6, -1, 4, 9, …
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11-2 Arithmetic Sequences
? Arithmetic Mean: A single arithmetic mean between two numbers is called the arithmetic mean. The arithmetic mean of the numbers a and b is
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11-2 Arithmetic Sequences
What is the arithmetic mean of: -4 and 8 17 and 20
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11-2 Arithmetic Sequences
A tougher kind of arithmetic sequence problem:
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11-2 Arithmetic Sequences
More examples.
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11-2 Arithmetic Sequences
Homework:
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