Illustration of ARITHMETIC SEQUENCE.pptx

Lesson on illustration of arithmetic sequence

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2. Lesson 2 Illustration of Arithmetic Sequence

3. Below are squares formed by matchsticks. 2. Count the number of matchsticks in each figure and record the results in a table. number of squares 1 2 3 4 number of matchsticks         Activity 1: What do we have in common?

4. number of squares 1 2 3 4 5 6 7 8 9 10 number of matchsticks                     Guide Questions: Is there a pattern in the number of matchsticks? If there is, described it. How is each term (number of matchsticks) found? What is the difference between any two consecutive terms?

5. number of squares 1 2 3 4 5 6 7 8 9 10 11 12 number of matchsticks  4 7 10  13   16 19 22  25  28  31  34 37 Notice that a constant number, 3, is added to each term to get the next term in the sequence. +3 +3 +3 +3 +3 +3 +3 +3 +3 +3 +3 34 37

6. http://www.virtualnerd.com/algebra-2/sequences-series/arithmetic/arithmetic-sequences/arithmetic-sequence-definition http://www.virtualnerd.com/algebra-2/sequences-series/arithmetic/arithmetic-sequences/common-difference-definition http://www.virtualnerd.com/algebra-2/sequences-series/arithmetic/arithmetic-sequences/sequence-common-difference-example

7. A sequence where each succeeding term is obtained by adding a fixed number is called an arithmetic sequence . The fixed number is called the common difference d . To identify if a pattern is an arithmetic sequence, we must examine consecutive terms. If all consecutive terms have a common difference you can conclude that the sequence is arithmetic.

8. To find the common difference , d , simply subtract the first term from the second term, a 2 – a 1 , or the second term from the third term, a 3 – a 2 , or the third term from the fourth term, a 4 – a 3 ; or in general, d = a n – a n – 1  

9. Illustrative example: 1. Determine if the sequence is arithmetic or not. If it is, find the common difference and the next three terms. -11, -4, 3, 10, …

10. Solution: To find out if the sequence is arithmetic, there must be a common difference between any two terms in the sequence. So that d = a 2 – a 1 = -4 – (-11) = 7 = a 3 – a 2 = 3 – (-4) = 7 = a 4 – a 3 = 10 – 3 = 7 The sequence is arithmetic, and the common difference is 7. The next three terms are obtained by adding 7 to the preceding term, so that a 5 = a 4 + 7 = 10 + 7 = 17 a 6 = a 5 + 7 = 17 + 7 = 24 a 7 = a 6 + 7 = 24 + 7 = 31

11. 2, 5, 8, 11,… 2, -4, 6, -8, 10,… -6, -10, -14, -18,… 40, 42, 44, 46,… 1.2, 1.8, 2.4,… 1, 5, 9, 13,… 8. … 9. 98, 95, 92, 89,… 10. 1,   Let’s try this one… Activity 2: Arithmetic or Not?

12. Sequence Yes No Common Difference 1. 12, 16, 20, 24, ….       2. 35, 32, 29, 26, …       3. 40, 45, 50, 55, …       4. -3. -23, -43, -63, …       5. 4, 9, 13, 17, …       6. -34, -64, -94, -124, …       7. -30, -40, -50, -60, …       8. -8, -3, 1, 4, …       9. -7, -9, -11, -13, …       10. 9, 14, 19, 24, …      

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