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Lesson 5 (3 rd 6 Weeks) TEKS 6.4 A/B

Arithmetic Sequences. Lesson 5 (3 rd 6 Weeks) TEKS 6.4 A/B. Sequence. A set of numbers written in a particular order .

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Lesson 5 (3 rd 6 Weeks) TEKS 6.4 A/B

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  1. Arithmetic Sequences Lesson 5 (3rd 6 Weeks)TEKS 6.4 A/B

  2. Sequence • A set of numbers written in a particular order. • For Example: 6, 10, 14, 18 is a sequence of four numbers. The number 6 is the first term in the sequence, 10 is the second term, 14 is the third term, and 18 is the fourth term.

  3. Arithmetic Sequence • A sequence of numbers where the difference between the successive terms is constant. • For Example: The first five terms of an arithmetic sequence are 3, 6, 9, 12, 15… The number 3 is the first term in the sequence, 6 is the second term, 9 is the third term, 12 is the fourth term, and 15 is the fifth term.

  4. The common difference in an arithmetic sequence can be identified by finding the difference between the terms in the sequence. +3 +3 +3 +3 3, 6, 9, 12, 15,…

  5. In the sequence 3, 6, 9, 12, 15,… the common difference is 3. +3 +3 +3 +3 3, 6, 9, 12, 15,…

  6. Follow these guidelines to find a rule or expression that can be used to find the nth term in an arithmetic sequence:

  7. Use the common difference to find a pattern that shows the relationship between the term’s position number and the value of the term. • Multiply the common difference and the position number. • Adjust by adding or subtracting to get the value of the term needed.

  8. 4. State the pattern as a rule. 5. Check to see whether the rule works for the next two terms in the sequence. 6. Represent the rule as an algebraic expression.

  9. Example 1:

  10. 1 x 3 = +3 2 x 3 = +3 3 x 3 = +3 4 x 3 = +3 5 x 3 = n x 3 The common difference of the “Value of the Term” is 3. Multiply the position number by the common difference.

  11. The pattern is “multiply the position number by 3 to get the value of the term.” • Written as an expression: n x 3 or 3n

  12. Example: Notice the numbers in the x column are successive. +3 +3 +3

  13. x 3 = +3 +3 • In the sequence 2, 5, 8, 11 …, the common difference is 3. • Multiply the common difference times the x-value. 1 x 3 = 3 • The first y-value is 2, not 3, therefore you must add or subtract from 3 to find the y-value (adjust). 3 -1 = 2 +3

  14. x 3 – 1 = x 3 – 1 = x 3 – 1 = • Maybe each y-value in this sequence is equal to 3 times its x-value an subtract 1. x • 3 - 1 = y or 3x – 1 = y • Check to see whether the rule works for the next two terms in the sequence. 2 x 3 -1 = 5 3 x 3 – 1 = 8 x 3 – 1 = x 3 – 1 =

  15. x 3 – 1 = x 3 – 1 = • Represent the rule as an algebraic expression. 3n - 1 x 3 – 1 = x 3 – 1 = x 3 – 1 =

  16. Example: +4 • Notice that the x-values are not successive until you get to the values of 5 and 6. You can only look for the common difference when the terms are successive.

  17. x 4 + 3 = x 4 = 4x + 3 x 4 + 3 = • Multiply 4 by the x values. Notice that when you do, you don’t get the y-values. • So you must add or subtract to get the y-values. • Check to see if the rule works. Then write it algebraic. x 4 + 3 = +4 x 4 + 3 =

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