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Published byMoris Jefferson Modified over 7 years ago

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**Sequences and Series 13.3 The arithmetic sequence**

DO NOW: Given the sequence 4, 15, 32, 55, 84, 119… Is it linear or quadratic? Write a recursive formula. Write an explicit formula.

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**Arithmetic Sequences Example #1**

a n or a(n) a) Write a recursive definition. b) Write a closed-form (explicit) definition. c) Common difference is ___. a n = a 1 + (n-1)d

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**Example #2: The 10th term of an arithmetic sequence is 146 and the 18th term is 98.**

Find the first term and common difference.

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**Example #3: A portion of the arithmetic sequence is given**

Example #3: A portion of the arithmetic sequence is given. Fill in blanks. 28, ___, ____, ____, 42 This is also known as finding the arithmetic means. “Find 3 arithmetic means between 28 and 42.”

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**Arithmetic Series & Sigma Notation Example #4: Write the finite series in Sigma Notation**

Finite series – also a partial sum. S4 = = 20

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**Example #5: Find the partial sum S10 of the first ten terms of the arithmetic sequence.**

an = 2 + (n-1) S10 = The sum of the first n terms, Sn , of the arithmetic sequence an , with common difference d is

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There’s MORE! If and a n = a 1 + (n-1)d , then Sn =

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**Find the sum of the first 75 terms of the sequence.**

Example #6: An arithmetic sequence has a1 = -10 and a common difference of 0.25. Find the sum of the first 75 terms of the sequence.

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**Arithmetic Series Arithmetic sequence – the list of terms 2,4,6,8,….2n**

Arithmetic series – the sum of the list …+ 2n +… Finite series – also a partial sum = 20 Infinite series …+ 2n +…

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