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Lesson 4.7: Arithmetic Sequences, pg. 233

Lesson 4.7: Arithmetic Sequences, pg. 233. Goals : To recognize arithmetic sequences. To extend and write formulas for arithmetic sequences. VOCABULARY. Sequence : a set of numbers in a specific order. Ex. 7 12 17 22 27 Terms : numbers in a sequence.

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Lesson 4.7: Arithmetic Sequences, pg. 233

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  1. Lesson 4.7: Arithmetic Sequences, pg. 233 Goals: To recognize arithmetic sequences. To extend and write formulas for arithmetic sequences.

  2. VOCABULARY • Sequence: a set of numbers in a specific order. Ex.7 12 17 22 27 • Terms: numbers in a sequence. • Arithmetic sequence: a numerical pattern that increases or decreases at a constant rate of value called the common difference. terms

  3. Common difference: difference between the terms. Ex. 7 12 17 22 27

  4. Example 1: Identify Arithmetic Sequences Determine whether each sequence is arithmetic. Justify your answer. • -15, -13, -11, -9, ……. This is an arithmetic sequence b/c the difference between the terms is constant. 2. This is not an arithmetic sequence b/c the difference between the terms is NOT constant.

  5. Your Turn • 24, 16, 8, 0, …. YES, -8 • 3, 6, 12, 24,……. NO, there is no common difference

  6. Writing Arithmetic Sequences Each term of an arithmetic sequence after the first term can be found by adding the common difference to the preceding term. An arithmetic sequence can be found as follows Where d is the common difference, is the first term is the second term.

  7. Ex. 2: Extend a Sequence • Find the next three terms of the arithmetic sequence -8, -11, -14, -17, ……… Common difference: -3 Next three terms: -20, -23, -26

  8. 7, 14, 21, 28,……. Common difference: 7 Next three terms: 35, 42, 49 • 34, 29, 24, 19,…… Common difference: -5 Next three terms: 14, 9, 4

  9. Nth Term of an Arithmetic Sequence The nth term of an arithmetic sequence with the first term and the common difference d is given by Nth term Common difference Nth term 1st term in the sequence where n is a positive integer.

  10. Ex. 3: Find a specific term • Find the 9th term in the arithmetic sequence 7, 11, 15, 19, ……..

  11. Find the 12th term of the arithmetic sequence 23, 25, 27, 29,……..

  12. =3, d=4, n=8 3.

  13. Write an equation for a sequence 1. Consider the arithmetic sequence -8, 1, 10, 19,….. a). Write and equation for the nth term of the sequence. b) Find the 12th term in the sequence.

  14. SUMMARY • Arithmetic sequence: a constant difference between terms. • Terms: numbers in a sequence • Common difference: the difference between the terms. NBA #11, page 236, problems 16-36 even

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