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- 1. 1
- 2. A sequence is a set of terms, in a definite order, where the terms are obtained by some rule. A finite sequence ends after a certain number of terms. An infinite sequence is one that continues indefinitely.
- 3. For example: 1, 3, 5, 7, … (This is a sequence of odd numbers) 1st term = 2 x 1 – 1 = 1 2nd term = 2 x 2 – 1 = 3 3rd term = 2 x 3 – 1 = 5 nth term = 2 x n – 1 = 2n - 1 . . . . . . + 2 + 2
- 4. NOTATION 1st term = u 2nd term = u 3rd term = u nth term = u . . . . . . 1 2 3 n
- 5. OR 1st term = u 2nd term = u 3rd term = u nth term = u . . . . . . 0 1 2 n-1
- 6. FINDING THE FORMULA FOR THE TERMS OF A SEQUENCE
- 7. A recurrence relation defines the first term(s) in the sequence and the relation between successive terms.
- 8. u = 5 u = u +3 = 8 u = u +3 = 11 u = u +3 = 3n + 2 . . . 1 2 3 n+1 For example: 5, 8, 11, 14, … 1 2 n
- 9. What to look for when looking for the rule defining a sequence
- 10. Constant difference: coefficient of n is the difference 2nd level difference: compare with square numbers (n = 1, 4, 9, 16, …) 3rd level difference: compare with cube numbers (n = 1, 8, 27, 64, …) None of these helpful: look for powers of numbers (2 = 1, 2, 4, 8, …) Signs alternate: use (-1) and (-1) -1 when k is odd +1 when k is even kk 2 3 n - 1
- 11. EXAMPLE: Find the next three terms in the sequence 5, 8, 11, 14, …
- 12. EXAMPLE: The nth term of a sequence is given by x = a) Find the first four terms of the sequence. b) Which term in the sequence is ? c) Express the sequence as a recurrence relation. 1__ 2 nn 1 1024 ____
- 13. EXAMPLE: Find the nth term of the sequence +1, -4, +9, -16, +25, …
- 14. EXAMPLE: A sequence is defined by a recurrence relation of the form: M = aM + b. Given that M = 10, M = 20, M = 24, find the value of a and the value of b and hence find M . n + 1 1 32 4
- 15. This powerpoint was kindly donated to www.worldofteaching.com http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.
- 16. 17 Do you find this slides were useful? One second of your life , can bring a smile in a girl life If Yes ,Join Dreams School “Campaign for Female Education” Help us in bringing a change in a girl life, because “When someone takes away your pens you realize quite how important education is”. Just Click on any advertisement on the page, your one click can make her smile. Eliminate Inequality “Not Women” One second of your life , can bring a smile in her life!! Do you find these slides were useful? If Yes ,Join Dreams School “Campaign for Female Education” Help us in bringing a change in a girl life, because “When someone takes away your pens you realize quite how important education is”. Just Click on any advertisement on the page, your one click can make her smile. We our doing our part & u ? Eliminate Inequality “Not Women”

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