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SEQUENCES AND SERIES

SEQUENCES AND SERIES. Arithmetic. Definition. When the difference between successive terms of a sequence is always the same number, the sequence is called arithmetic. This difference is called the common difference and is denoted with a d. Examples.

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SEQUENCES AND SERIES

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  1. SEQUENCES AND SERIES Arithmetic

  2. Definition When the difference between successive terms of a sequence is always the same number, the sequence is called arithmetic. This difference is called the common difference and is denoted with a d.

  3. Examples The following sequences are arithmetic: • 2, 6, 10, 14, 18, … difference = 4 • 17, 10, 3, -4, -11, … difference = -7

  4. Formula The formula for the nth term of a general arithmetic sequence is:

  5. Examples • Find a formula for the nth term of the arithmetic sequence 3, 5, 7, … 2. Find the number of multiples of 3 between 25 and 332.

  6. Examples • Find a formula for the nth term of the arithmetic sequence 3, 5, 7, … 2. Find the number of multiples of 3 between 25 and 332.

  7. Examples Continued 3. In an arithmetic sequence, a2=2 and a5=17. Find a10. 4. How many terms are in the sequence 4, 6.5, …, 119?

  8. Examples Continued 3. In a arithmetic sequence, a2=2 and a5=17. Find a10. 4. How many terms are in the sequence 4, 6.5, …, 119?

  9. Definition A series is an indicated sum of the terms of a sequence. • Finite Sequence: 2, 6, 10, 14 • Finite Series: 2 + 6 + 10 + 14

  10. Formula The sum of the first n terms of an arithmetic series is:

  11. Example • Find S25 of the arithmetic series 11 + 14 + 17 + 20+ …

  12. Example • Find S25 of the arithmetic series 11 + 14 + 17 + 20+ … First you have to find the 25th term. Now you can find the sum of the first 25 terms.

  13. Examples Continued • Find the sum of the arithmetic series 5+9+13+…+153.

  14. Examples Continued • Find the sum of the arithmetic series 5+9+13+…+153. First you must determine how many terms you are adding. Now you can find the sum of the first 38 terms.

  15. Assignment RED BOOK Page 849 Problems 13 – 41 odd, 51

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