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Arithmetic and geometric_sequences

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Arithmetic and geometric_sequences

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Arithmetic and geometric_sequences

  1. 1. REVIEW Create a line graph for the following interval ( -6, 3] or [7, - 11) ARITHMETIC AND GEOMETRIC SEQUENCES
  2. 2. ARITHM ETIC AND GEOM ETRIC SEQUENCES ARITHMETIC AND GEOMETRIC SEQUENCES
  3. 3. SEQUENCE A sequence is an ordered list of numbers that often form a pattern. Each number in the list is called a term of sequence. Describe the pattern in the following sequences and write the next two terms a.) 5,11,17,23 c.) 400, 200, 100, 50 b.) 2, -4, 8, -16 d.) -15, -11, -7, -3 ARITHMETIC AND GEOMETRIC SEQUENCES
  4. 4. ARITHMETIC SEQUENCE In an arithmetic sequence, the difference between consecutive terms is constants. This difference is called the common difference. Example: 3, 8, 13, 18 ARITHMETIC AND GEOMETRIC SEQUENCES
  5. 5. ARITHMETIC SEQUENCE Tell whether the sequence is arithmetic. If it is, what is the common difference? a.) 8, 15, 22, 30 b.) 7, 9, 11, 13 c.) 10, 4, -2, -8 d.) 2, -2, 2, -2 ARITHMETIC AND GEOMETRIC SEQUENCES
  6. 6. RECURSIVE AND EXPLICIT FORMULA Let n= the term number in the sequence Let A(n) = the value of the nth term of the sequence Let d= the common difference Recursive Formula Explicit Formula A(n) = A( n – 1) + d A(n) = A(1) + (n – 1)d ARITHMETIC AND GEOMETRIC SEQUENCES
  7. 7. RECURSIVE AND EXPLICIT FORMULA Example: An arithmetic sequence is represented by the recursive formula A(n) = A (n – 1) + 12. If the first sequence is 19, write the explicit formula. ARITHMETIC AND GEOMETRIC SEQUENCES
  8. 8. RECURSIVE AND EXPLICIT FORMULA An arithmetic sequence is represented by the explicit formula A(n) = 32 + (n – 1) (22). What is the recursive formula? ARITHMETIC AND GEOMETRIC SEQUENCES
  9. 9. RECURSIVE AND EXPLICIT FORMULA 1.) Write a recursive formula for the sequence: 99, 88, 77, 66 2.) Write a recursive formula for the explicit formula: A(n) = 5 + (n -1) (3) 3.) Find the 2nd , 4th , and 11th term: A(n) = - 3+ (n – 1) (5) ARITHMETIC AND GEOMETRIC SEQUENCES
  10. 10. RECURSIVE AND EXPLICIT FORMULA Write a recursive and an explicit formula for the arithmetic sequence: 9, 7, 5, 3, 1 Find the 7th and 11th term ARITHMETIC AND GEOMETRIC SEQUENCES
  11. 11. RECURSIVE AND EXPLICIT FORMULA Find the second, third, and fourth terms of the sequence. Then write the explicit formula that represents the sequence A(n) = A (n – 1) – 1 ; A(1) = 8 ARITHMETIC AND GEOMETRIC SEQUENCES

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