Geometric Sequences A geometric sequence is a list of numbers with a common ratio symbolized as r. This means that you can multiply by the same amount.

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Presentation transcript:

Geometric Sequences A geometric sequence is a list of numbers with a common ratio symbolized as r. This means that you can multiply by the same amount to get from one term to the next. Each term is signified as an. Find the common ratio in the following sequence: 3, 9, 27, 81, 243, … Find the next five terms of a sequence: a1=6, r = 2

FORMULAS Explicit : 𝒂 𝒏 = 𝒂 𝟏 𝒓 𝒏−𝟏 Recursive: 𝒂 𝟏 =# 𝒂 𝟏 = 𝒂 𝒏−𝟏 ∙𝒓 1) What would be the explicit and recursive formulas for the first example? 3, 9, 27, 81, 243, … 2) What would be the explicit and recursive formulas for the second example? a1 =6, r = 2

3) Given the sequence defined by the explicit formula 𝑎 𝑛 =3 ∙ 1 2 𝑛−1 what is the common ratio and first 4 term of the sequence? 4) Given the sequence defined by the recursive formula 𝑎 1 =4 𝑎 𝑛 = 𝑎 𝑛−1 ∙−2 What is the common ratio and first 4 terms of the sequence?