Objectives

​Understand the properties of geometric sequences related to

• Three consecutive terms

• Transformations of the terms

Property 1: Relation among 3 consecutive terms​

------- two ways to find the common ratio

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------- cross multiply to obtain the relationship​

​Example 1

​--------- two possible answers obtained from a quadratic equation.

​Example 2

​--------- use algebra to express the three terms of the arithmetic sequence

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​--------- form a geometric sequence after applying the changes

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​--------- apply the property of 3 consecutive terms to find the unknown

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Property 2: Transformation of the terms

​For example,

2, 6, 18, 54 ... is a geometric sequence. After multiplying each term by the same constant, it remains as a geometric sequence.

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multiply each term by 2: 4, 12, 36, 108 ... is still a geometric sequence

multiply each term by 0.5: 1, 3, 9, 27​ ... is still a geometric sequence