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# TechMathII - 1.2 - Sequences

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### TechMathII - 1.2 - Sequences

1. 1. Bell Ringer <ul><li>Write in order from least to greatest. </li></ul><ul><li>1) -4/9, -2/5, -5/14 </li></ul><ul><li>2) -6/14, -5/8, -21/45 </li></ul><ul><li>3) 1/11, 2/19, 5/25 </li></ul>
2. 2. Vocabulary <ul><li>Sequences : numerical patterns in which the numbers are arranged in a certain order </li></ul><ul><li>Terms : the numbers in a sequence </li></ul>
3. 3. Continuing and Identifying a Pattern Ex 1: <ul><li>What is the perimeter (distance around) of the first figure: </li></ul><ul><li>What is the perimeter of the second figure? </li></ul><ul><li>What is the pattern in the perimeter of the figures? </li></ul><ul><li>What is the perimeter of the 6 th and 10 th figures? </li></ul>
4. 4. Arithmetic Sequences <ul><li>- When the difference between two consecutive terms of a sequence is the same </li></ul><ul><li>“ adding the same amount each time” </li></ul><ul><li>- Common Difference </li></ul>
5. 5. Examples <ul><li>Find the next three terms in each arithmetic sequence. </li></ul><ul><li>1) 25, 37, 49, 61, … </li></ul><ul><li>2) 5, 11, 17, 23, … </li></ul><ul><li>3) Z, ZYY, ZYXX, ZYXWW, … </li></ul><ul><li>4) A, AA, AAB, AABB, AABBC, … </li></ul>
6. 6. You try 1! Find the next three terms in each arithmetic sequence. <ul><li>1) -2, 5, 12, 19, … </li></ul><ul><li>2) 135, 122, 109, … </li></ul><ul><li>3) 1/8, ¼, 3/8, ½, … </li></ul><ul><li>4) -21, -32, -43, … </li></ul>
7. 7. Geometric Sequences <ul><li>- Each term is multiplied by a common number or factor to obtain the next term </li></ul><ul><li>“ multiplying by the same amount each time” </li></ul><ul><li>- Common Ratio </li></ul>
8. 8. Examples <ul><li>Find the next three terms in each geometric sequence. </li></ul><ul><li>1) 48, 24, 12, 6, … </li></ul><ul><li>2) 3, 15, 75, 375, … </li></ul><ul><li>3) 1, ½, ¼, … </li></ul><ul><li>4) 352, -176, 88, -44, … </li></ul>
9. 9. You try 2! Find the next three terms in each geometric sequence. <ul><li>1) 1, -1, 1, -1, … </li></ul><ul><li>2) 135, 45, 15, … </li></ul><ul><li>3) 6, 30, 150, … </li></ul><ul><li>4) 22500, 4500, 900, … </li></ul>
10. 10. You try 3! Decide whether each sequence is arithmetic or geometric. Then find the next three terms in each sequence. <ul><li>1) 1, 2, 4, 8, … </li></ul><ul><li>2) 13, 9, 5, … </li></ul><ul><li>3) 16, -4, 1, … </li></ul><ul><li>4) -5, 0, 5, 10, … </li></ul>
11. 11. Homework <ul><li>Sequences WS </li></ul>