F6 Ch2.2 Properties of Geometric Sequences

​ch2.2 Properties of Geometric Sequences

Independent study

Objectives

​Understand the properties of geometric sequences related to

• Three consecutive terms

• Transformations of the terms

Draw

Review: How to find the general term of a geometric sequence?

Fill in the Blanks

8, a, 200 ... form a geometric sequence. Find a possible value of the second term a.

Multiple Select

10, a, 2250 ... form a geometric sequence. Find the possible value(s) of a.

• 15

• 150

• -150

• -15

Property 1: Relation among 3 consecutive terms​

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

​

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

​Example 1

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

Multiple Select

• 2

• -2

• $$\frac{7}{9}$$  

• $$\frac{9}{7}$$  

​Example 2

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

​

​

​

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

​

​

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

​

​

Multiple Select

• 8

• -2

• 6

• -5

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.

​

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

Multiple Select

a, b, c, ... is a geometric sequence. Choose all geometric sequences.

• 2a, 2b, 2c ...

• -100a, -100b, -100c ...

• 7a, 8b, 9c ...

• -3a, -3b, 3c ...

Multiple Select

$$\frac{a}{3},\ \frac{b}{9},\ \frac{c}{27}...$$   is a geometric sequence. Choose all geometric sequences.

• $$a,\ b,\ c\ ...$$  

• $$3a,\ b,\ \frac{c}{3}...$$  

• $$9a,\ 3b,\ c...$$  

• $$c,\ b,\ a\ ...$$  

Open Ended

Write down one fact about geometric sequences that you have learned during this quizizz lesson.