(1)SEQUENCE.pptx
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The document defines sequences as sets of numbers governed by a rule or pattern. Finite sequences have a limited number of terms with a known last term, while infinite sequences have countless terms continuing without end. Examples are provided of finite and infinite sequences. The document explains how to determine the next term in a sequence given prior terms, and asks readers to list the first five terms of sample sequences and identify them as finite or infinite.
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(1)SEQUENCE.pptx
- 2. OBJECTIVES Define sequence, finite and infinite sequence. List the next few terms given several consecutive terms of a sequence. Appreciate the concept of generating patterns.
- 3. SEQUENCE is a set of numbers that are governed by a certain rule or that follow a certain pattern. is a functions whose domain is the set of positive integers or a finite subset of positive integers.
- 4. SEQUENCE Each number in the list is called a term. EXAMPLES: Sequence 1 Sequence 2 2,4,6,8,10 2,4,6,8,10,… Term 1, 2, 3, 4, 5 Term 1, 2, 3, 4, 5 Domain – relative position of each term (1,2,3,4,5) Usually begins with position 1 unless otherwise stated. Range – the actual “terms” of the sequence (2,4,6,8,10)
- 5. SEQUENCE CAN BE FINITE OR INFINITE FINITE INFINITE 1, 3, 5, 7 6,12, 18, 24, … 20, 40, 60, 80 7, 14, 21, 28, … 5, 10, 15, …, 60 1, 8, 27, 64, 125, …
- 6. SEQUENCE CAN BE FINITE OR INFINITE Finite Sequence is a sequence that contains a limited number of terms. It means that the last term of the sequence is known. Example: 2, 4, 6, 8, 10 and 3, 6, 9, 12, 15, 18
- 7. SEQUENCE CAN BE FINITE OR INFINITE Infinite Sequence is a sequence that contains a countless number of terms. The number of the term in sequence continues or it has no end. The ellipsis (…) to the end of the sequence shows that the sequence is infinite. Example: 1, 3, 5, 7, 9, … and 1, 2, 3, 5, 6, 7, …
- 8. EXAMPLE Determine how the next term in each sequence can be found. Then find the next term in the sequence. 1. 7, 14, 21, 28, ___ 2. 1, 3, 9, 27, ___ 3. 5, -6, -17, -28, ___ 4. 𝟐, 𝟏 𝟐 , 𝟏 𝟖 , 𝟏 𝟑𝟐 , ___
- 9. Boards Up! Write at least the first 5 terms of the following sequence, then tell whether the sequence is finite or infinite sequence. 1. Counting number from 1 – 20. 2. Multiples of 3. 3. Even numbers from 4 – 100. 4. Odd numbers. 5. Prime numbers from 2.
- 10. Examples: 1. The table below shows the cost of renting the Cavite Hall at Island Cove Resort and Leisure Park in Kawit, Cavite depending on the number of attendees. Number of Persons Rental Cost in Peso 20 6200 25 6500 30 6800 35 7100
- 11. SEATWORK 1: 1. It is an ordered of numbers that follows a pattern or rule. a. Sequence b. Series c. Algebra d. Geometry
- 12. SEATWORK 1: 2. What are the next 3 terms of the sequence 2, 4, 6, __, __, __. a. 1, 2, 3 b. 8, 10, 12 c. 3, 4, 5 d. 3, 5, 7
- 13. SEATWORK 1: 3. Which of the following sequence illustrates an infinite sequence. a. 1, 2, 3, 4, 5, … 10 b. 2, 4, 6, 8, 10 c. 3, 6, 9, 12, 15, …. d. 5, 10, 15, 20, 25
- 14. SEATWORK 1: 4. The sequence 1/3, 1/6, 1/9, 1/12, 1/15 is an example of a finite sequence. a. True b. False c. Maybe d. I don’t know
- 15. SEATWORK 1: 5. It is a symbol that tells you that the sequence is infinite. a. Greater than b. Less than c. Equal d. Ellipsis