Arithmetic & Geometric Sequences

Definition Arithmetic Sequence If a sequence of values follows a pattern of adding a fixed amount from one term to the next, it is referred to as an  arithmetic sequence. General Rule an = a1 + (n – 1)d a1 is the first term and d is the common difference.

Definition Geometric Sequence A geometric sequence is a sequence where each term is found by multiplying or dividing the same value from one term to the next. We call this value "common ratio" General Rule an = a1 (r)n-1 a1 is the first term & r is the common ratio

What is an arithmetic sequence? A sequence in which each term is found by ADDING the same number to the previous term. 4, 8, 12 , 16, 20………….. +4 +4 +4 +4

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

What is a geometric sequence? A sequence in which each term can be found by multiplying the previous term by the same number. 3, 9, 27 , 81, 243………….. x3 x3 x3 x3

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

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