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13.1 – Finite Sequences and Series

13.1 – Finite Sequences and Series. Essential Question: What is the difference between an arithmetic and a geometric sequence?. Vocabulary. Sequence – a set of #’s or terms arranged in a particular order. Arithmetic Sequence – the difference of any 2 consecutive terms is constant.

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13.1 – Finite Sequences and Series

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  1. 13.1 – Finite Sequences and Series Essential Question: What is the difference between an arithmetic and a geometric sequence?

  2. Vocabulary • Sequence – a set of #’s or terms arranged in a particular order. • Arithmetic Sequence – the difference of any 2 consecutive terms is constant. (common difference, + or – ) • When you add the same number to each term. (NOTE: you can add a negative which looks like subtraction.)

  3. Vocab. • Geometric Sequence – the ratio of any 2 consecutive terms is constant. (common ratio, × or ÷ ) • When you multiply each term by the same number. (NOTE: you can multiply by a rational number as well as a whole number.)

  4. We use the notation to talk about the “n”th term. • Formulas for the “n”th term are as follows:

  5. Arithmetic Sequence Common Difference To get the “n”th term The “n” term 1st term

  6. Geometric Sequence The “n” term To get the “n”th term Common Ratio 1st term

  7. Example Find a formula for tn and sketch the graph. • 1, 4, 7, 10, … • 8, 4, 2, 1, …

  8. Example • State whether the given sequence is arithmetic, geometric, or neither. Find a formula for tn in terms of n, and evaluate t8. a. b. c. 15, 11, 7, 3, …

  9. Example In a certain sequence, t2 = 2 and t5 = 16. Find t10 if the sequence is: • arithmetic • geometric

  10. Example • Find the # of multiples of 7 between 30 and 300.

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