A sequence is a set of ordered numbers. There are two types of sequences - Arithmetic Sequences and Geometric Sequences.
ARITHMETIC SEQUENCE An arithmetic sequence is a sequence of numbers that increase or decrease at a constant rate. In an arithmetic sequence, the difference between each number is called the common difference. Example 1: Look at the sequence 3, 6, 9, 12, 15, ...... What is the common difference? What is the difference between 3 and 6? Between 6 and 9? Between 9 and 12? Is it the same each time? YES! The difference between each number is 3. The common difference is 3! A variable expression can be written to express the relationship between the two consecutive terms of a sequence. The variable expression for Example 1 is n + 3. GEOMETRIC SEQUENCE An geometric sequence is a sequence formed by multiplying the same number to each term. In a geometric sequence, the number is term is multiplied by is called the common ratio. Example 2: Look at the sequence 3, 6, 12, 24, 48, ...... What is the common ratio? What number do you multiply by 3 to get 6? By 6 to get 12? By 12 to get 24? Is it the same each time? YES! The number multiplied is 2. The common ratio is 2! Like the arithmetic sequence, a variable expression can be written to express the relationship between the two consecutive terms of a geometric sequence. The variable expression for Example 2 is 2n. |
Click on the Virtual Nerd Video button below to watch a video about how to determine if a sequence is Arithmetic or Geometric.
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