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Arithmetic and Geometric Sequences Sequences Numbers can be written in a pattern, such as the following: 3,9,27, 81…. Do you know the pattern? Everything is being multiplied by 3. A number pattern can be referred to as a sequence. There are two types of sequences: an arithmetic sequence and a geometric sequence. Number Patterns The numbers in a sequence are called terms of the sequence. An arithmetic sequence is formed by adding a fixed number to each previous term. This number is called the common difference. What is an arithmetic sequence? A sequence in which each term is found by ADDING the same number to the previous term. +4 4, +4 +4 +4 8, 12 , 16, 20………….. What is the common difference? The difference between each number. This determines what is added to each previous number to obtain the next number. 4, 8, 12, 16, 20………….. 4 is the common difference A. B. C. Arithmetic Sequences Find the common difference of each arithmetic sequence. a. -7, -3, 1, 5 b. 17, 13, 9, 5 c. Common difference is 4. d. Common difference is -4. Special Note: If there is no common difference, the sequence is not arithmetic. Geometric Sequences You form a geometric sequence by multiplying a term in the sequence by a fixed number to find the next term. The fixed number is the common ratio. What is a geometric sequence? A sequence in which each term can be found by multiplying the previous term by the same number. x3 3, x3 x3 x3 9, 27 , 81, 243………….. What is the common ratio? The number used to multiply by each previous number to obtain the next number. 2, 8, 32, 128, 512………….. 4 is the common ratio What is the next term in this sequence? x4 x4 x4 x4 5, 20, 80, 320 , _____ 1,280 What is the next term in this sequence? X-2 X-2 X-2 X-2 -3, 6, -12, 24 , _____ -48 Is this an arithmetic or geometric sequence? 10, 15, 20, 25, 30…… Arithmetic Sequence +5 5 is the common difference Is this an arithmetic or geometric sequence? 2, 12, 72, 432, 2,592…… Geometric Sequence x6 6 is the common ratio A. B. C. D. Sequence 1 Sequence 2 Sequence 3 Sequence 4