GenerartingPatterns.pptx for Grade 10 Matheamtics
- 2. Let’s Start! 1. 1, 3, 5, 7, _, _, _ 2. 5, 15, 25, _, _, _ 3. A, D, G, J, _, _, _ 4. 1, 4, 9, 16, 25, _, _, _ 5. 1, 3, 6, 10, _, _, _ Find the next three terms
- 3. What Is a Sequence? A sequence is a set of objects which is listed in a specific order, one after another.
- 4. What Is a TERM? Each member or element in the sequence.
- 5. The terms in a sequence can be written as , , 𝒂𝟏 𝒂𝟐 , , . . . , , . .. which 𝒂𝟑 𝒂𝟒 𝒂𝒏 means 1 is the first term, 2 𝑎 𝑎 is the second term, 3 is the 𝑎 third term, …, is the nth 𝑎𝑛 term, and so on.
- 6. What Is a FINITE SEQUENCE? A finite sequence contains a limited number of terms. This means it has an end or last term.
- 7. EXAMPLES: a) Days of the week: { , 𝑆𝑢𝑛𝑑𝑎𝑦 , , . . . , 𝑀𝑜𝑛𝑑𝑎𝑦 𝑇𝑢𝑒𝑠𝑑𝑎𝑦 } 𝑆𝑎𝑡𝑢𝑟𝑑𝑎𝑦 b) First 10 positive perfect squares: {1, 4, 9, 16, 25, 36, 49, 64, 81, 100 }
- 8. What Is aN INFINITE SEQUENCE? an infinite sequence contains a countless number of terms. The number of terms of the sequence continues without stopping or it has no end term.
- 9. EXAMPLES: a) Counting numbers: {1, 2, 3, 4, 5, . . .} b) Multiples of 5: {5, 10, 15, 20, 15, . . .}
- 10. WHAT IS GENERAL TERM? a formula that expresses any term in the sequence in terms of its position (n) in the sequence
- 11. EXAMPLE: An = 2n The general term can be written as: an = 2n. The general term can be written as: an = 2n.
- 12. EXAMPLE: Find the first five terms of the sequence with the general term an = 2n The general term can be written as: an = 2n. The general term can be written as: an = 2n.
- 13. EXAMPLE: Find the first five terms of the sequence with the general term an = 2n-1 The general term can be written as: an = 2n. The general term can be written as: an = 2n.
- 14. EXAMPLE: Find the first five terms of the sequence with the general term an = 2-3n The general term can be written as: an = 2n. The general term can be written as: an = 2n.
- 15. EXAMPLE: Find the first five terms of the sequence with the general term an = (n-3)^n The general term can be written as: an = 2n. The general term can be written as: an = 2n.
- 16. EXAMPLE: Find the first five terms of the sequence with the general term an = (-1)^n The general term can be written as: an = 2n. The general term can be written as: an = 2n. 2n-1
- 17. ACTIVITY NO.1 Find the first five terms of the sequence with the general term: The general term can be written as: an = 2n. The general term can be written as: an = 2n. 1. an= n+4 2. an= 3n-1 3. an=12-3n 4. an=3^n 5. an=(-2)^n
- 18. QUIZ No.1 Find the first five terms of the sequence with the general term: The general term can be written as: an = 2n. The general term can be written as: an = 2n. 1. an= 7n-3 2. an= 11-9n 3. an=5n+6 4. an= 5n-3 5. an= 11- 9n 6n+2 n^2+3