Geometric Series

​​Routines

​​Review

​Workplan

Discussion

I.P Activity

Arithmetic or Geometric

​

B.B. Activity

Discussion

Big Ideas

" The ability to organize and sequence things helps us manage our time effectively."

Enduring Understanding

"Why must patterns be simplified?" 

Multiple Choice

Find the common ratio: 16, 8, 4, 2, ...

• r = 2
• r = 8
• r = 1/4
• r = 1/2

Multiple Choice

The next term of the sequence 2,4,8,16 is

• 64

• 32

• 108

• 20

Multiple Choice

$$a_n=a_1r^{n-1}$$  

Given the formula for a geometric sequence , r stands for

• common difference

• wanted term

• common ratio

• first term

Multiple Choice

What is the common ratio of the geometric sequence -2, -8, -32, -128, ...?

• -4

• 4

• -2

• 2

Multiple Choice

Solving for the nth term of geometric sequence, given that a₁ = 4 and r= 6, what is the value of the 4th term?

• 144

• 864

• 124

• 764

Geometric or Arithmetic?

Multiple Choice

-2, -10, -50, -250, ...

• Arithmetic

• Geometric

Multiple Choice

-1, 6, -36, 316, ...

• Arithmetic

• Geometric

Multiple Choice

-1, -5, -25, -125, ...

• Arithmetic

• Geometric

Multiple Choice

29, 38, 47, 56, ...

• Arithmetic

• Geometric

Multiple Choice

-8, 22, 52, 82, ...

• Arithmetic

• Geometric

"Geometric Series"

The sum of the terms of a geometric sequence is called a geometric series. The values of the term diverges.
Formula:

​Finite Geometric Series

The sum of the terms of a geometric sequence is called a geometric series. The values of the term converges.
Formula:

​Infinite Geometric Series

Multiple Choice

Which of the following is DIVERGENT?

• 2+4+8+16+...

• 25+5+1+0.2+...

• 100+50+25+5+...

• 3(.25)ⁿ = A_n

Multiple Choice

Determine whether the sequence is convergent or divergent:

a_n=2 (⅓)^n-1

• Convergent

Multiple Choice

Is the sequence convergent or divergent?

• Convergent

"Brain Break"

​Examples: Determine the sum of the first 6 terms of the following geometric sequences.

​Finite Geometric Sequence

​2. ​ 3, 6, 12, 24, ....

Multiple Choice

Find the sum of the first 10 terms of a geometric sequence 5, 10, 20, ...

• 5115

• 5114

• 5113

• 5112

Multiple Choice

What is the sum of the first 8 terms of the geometric sequence: 1 , 3 , 9 , 27 , . . . ?

• 3,260

• 3,270

• 3,280

• 3,290

Multiple Choice

Find the sum of the n terms when a₁=4 , r = -5 and n = 4 .

• 416

• 832

• 775

• -775

The sum of the terms of a geometric sequence is called a geometric series. The values of the term converges.
Formula:

​Infinite Geometric Series

​Examples: Evaluate the following infinite geometric series.

a. -8, -4, -2,....
b. 8+ 4+ 2+1 + 1/2, ...

Multiple Choice

Evaluate the infinite series described: 

• 20/3
• No Sum
• 21/5
• 4/3

Multiple Choice

Evaluate the infinite series described: 

• No Sum
• 32/3
• 2/3
• 34/3

Multiple Choice

Evaluate the infinite geometric series:

1 + 1/5 + 1/25 + ...

• 5/4

• 9/5

• 5/6

• 65/27

Enduring Understanding

"Why must patterns be simplified?" 

Groupings

"M.L. Activity"