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Arithmetic Sequences

Arithmetic Sequences. An Arithmetic Sequence is defined as a sequence in which there is a common difference between consecutive terms. Which of the following sequences are arithmetic ? Identify the common difference. YES. YES. NO. NO. YES.

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Arithmetic Sequences

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  1. Arithmetic Sequences

  2. An Arithmetic Sequence is definedas a sequence in which there is a common difference between consecutive terms.

  3. Which of the following sequences are arithmetic? Identify the common difference. YES YES NO NO YES

  4. The common difference is always the difference between any term and the term that proceeds that term. Common Difference = 5

  5. The general form of an ARITHMETIC sequence. First Term: Second Term: Third Term: Fourth Term: Fifth Term: nth Term:

  6. Formula for the nth term of an ARITHMETIC sequence. If we know any three of these we ought to be able to find the fourth.

  7. Given: Find: IDENTIFY SOLVE

  8. Given: Find: What term number is -169? IDENTIFY SOLVE

  9. Find: Given: What’s the real question? The Difference IDENTIFY SOLVE

  10. Find: Given: IDENTIFY SOLVE

  11. Arithmetic Series Geometric Series Sum of Terms Sum of Terms An introduction………… Arithmetic Sequences Geometric Sequences ADD To get next term MULTIPLY To get next term

  12. Find the next four terms of –9, -2, 5, … Arithmetic Sequence 7 is referred to as the common difference (d) Common Difference (d) – what we ADD to get next term Next four terms……12, 19, 26, 33

  13. Find the next four terms of 0, 7, 14, … Arithmetic Sequence, d = 7 21, 28, 35, 42 Find the next four terms of x, 2x, 3x, … Arithmetic Sequence, d = x 4x, 5x, 6x, 7x Find the next four terms of 5k, -k, -7k, … Arithmetic Sequence, d = -6k -13k, -19k, -25k, -32k

  14. Vocabulary of Sequences (Universal)

  15. Given an arithmetic sequence with x 38 15 NA -3 X = 80

  16. 1.5 x 16 NA 0.5 Try this one:

  17. 9 633 x NA 24 X = 27

  18. -6 20 29 NA x

  19. The two arithmetic means are –1 and 2, since –4, -1, 2, 5 forms an arithmetic sequence Find two arithmetic means between –4 and 5 -4, ____, ____, 5 -4 5 4 NA x

  20. The three arithmetic means are 7/4, 10/4, and 13/4 since 1, 7/4, 10/4, 13/4, 4 forms an arithmetic sequence Find three arithmetic means between 1 and 4 1, ____, ____, ____, 4 1 4 5 NA x

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