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Sequences

Sequences. Tuesday December 18, 2012. WARM UP. Describe the pattern and write the next 3 terms. a) 3, 6, 12, 24, ... b) 1, 2, 4, 7, 11, 16, ... c) 2, 5, 10, 17, 26, . Definitions. Sequence – a set of numbers, separated by commas, arranged in an order.

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Sequences

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  1. Sequences Tuesday December 18, 2012

  2. WARM UP Describe the pattern and write the next 3 terms. a) 3, 6, 12, 24, ... b) 1, 2, 4, 7, 11, 16, ... c) 2, 5, 10, 17, 26, ...

  3. Definitions • Sequence – a set of numbers, separated by commas, arranged in an order. • Term - a number in a sequence. Subscripts are usually used to identify the position of the terms • First term: t1 • Second term: t2 • Third term: t3 • nth term: tn • A sequence may stop or continue indefinitely • Discrete Sequence: 5, 7, 9, 11 • Continuous Sequence: 80, 40, 20, 10, … (dots indicate that sequence is continuing indefinitely) t1 , t2 , t3 , …. tn

  4. Real world applications Archimedean Spiral t1 = 1 t2 = 2 t3 = 3 t4 = 4 Spirals Sea shells Cyclones Snail shells Finger tips Galaxy Etc. Exponential Spiral t1 = 1 t2 = 2 t3 = 3 t4 = 4

  5. General Term • A formula or rule, labelled tn, that expresses each term of a sequence as a function of its position, n.

  6. Example 1 a) Determine the general term for the sequence 3, 5, 7, 9, … • Use trial and error for now. • Write a General Term: tn = b) What would the 37th term be?

  7. Example 2 a) Determine the general term for the sequence 1, 3, 5, 7, 9, … • Use trial and error for now. • Write a General Term: tn = b) What would the 100th term be?

  8. Example 3 a) Determine the general term for the sequence 1, 3, 9, 27, … • Use trial and error for now. • Write a General Term: tn = b) What would the 55th term be?

  9. Example 4 a) Write the first 5 terms of the sequence tn = 3n - 2 b) Given the formula for the nth term, f(n) = 2n2 - 1 in function notation, find t8.

  10. Arithmetic Sequences

  11. Arithmetic Sequences • A sequence that has the same difference, the common difference, between any pair of consecutive terms. General Term: a- first term d- common difference n- term number

  12. Example 5 • Determine a formula that defines the arithmetic sequence 3, 12, 21, 30, … • Write a General Term: tn = b) What would the 27th term be?

  13. Example 6 What is the 33rd term of the sequence 18, 11, 4, -3, …

  14. Example 7 The 7th term of an arithmetic sequence is 53 and the 11th term is 97. Determine the 100th term.

  15. Example 8 Find the number of terms there are in the sequence: -3, 2, 7, …, 152

  16. Example 9 The rates of a mini grand-prix race are $7 for a license fee and $3 per lap. • What would the rate for 10 laps be? • How many laps can you do with $22?

  17. HOMEFUN!! • Worksheet – Sequences • Textbook 7.1 Pg. 424 – 425, #5 – 12, 15

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