Sequences and Series 13.3 The arithmetic sequence

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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

• n 1 2 3 4 5
• a n or a(n) 5 9 13 17 21
• 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. 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 2 4 6 8 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)3 S10
• The sum of the first n terms, Sn , of the
  arithmetic sequence an , with common difference d
  is

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Theres MORE!
If and a n a 1 (n-1)d , then Sn
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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
• 2 4 6 8 2n
• Finite series also a partial sum
• 2 4 6 8 20
• Infinite series - 2 4 6 8 2n